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00:00Four persons are chosen at random from group containing three men, two women and four children.
00:07What is chance that exactly two of them will be children?
00:11So how many children have children?
00:15Okay, how many people are talking about?
00:17Three men, two women, four children.
00:20So one thing is that we have total four people to slack.
00:22Nine combinations, four people have total outcome.
00:25So we have total outcome.
00:27So three men, two women and four children.
00:31So men are two.
00:32And the rest of the children, two children, four combinations, four combinations, two.
00:38Men and women will get five.
00:40And we need two.
00:41So five combinations, two.
00:43Four combinations, two, six.
00:45Five combinations, two, ten.
00:46So six, ten.
00:48This will cut.
00:49From six tables.
00:51So it will be ten upon twenty.
00:53What option is you are up?
00:55You are up.
00:56It was very simple that x plus y is greater than fifteen.
00:59Okay.
01:00Okay.
01:00So we have all those numbers.
01:02These two are x here and y here.
01:04They are looking for pluses.
01:05They are looking for more than fifteen.
01:07So one is five plus twelve.
01:11Then seven plus ten, seven plus twelve.
01:13Nine plus eight, nine plus ten, nine plus eleven.
01:15Eleven plus six.
01:17So three from ten.
01:19There is no one at least.
01:20Five from one.
01:21So one is 15.
01:22So one is 15.
01:23So the answer is 15 of these.
01:24All are asking this.
01:25One is equal to fifteen.
01:26One is equal to fifteen.
01:28So equal to fifteen.
01:30Okay.
01:31Equal to fifteen is an important thing.
01:33So here.
01:34You have only three plus twelve.
01:37One is equal to fifteen.
01:39See.
01:40Five plus ten.
01:42Okay?
01:44This is also 15.
01:467 plus 8
01:49This is also 15.
01:519 plus 6
01:53This is also 15.
01:55This is also 15.
01:57There are 5 events.
01:59And when the events are less than 15,
02:01you can also get out of it.
02:03Less than 15, there will be more than 3.
02:05Just think about it.
02:07Because it is a small number.
02:09If you have 3 plus 12,
02:11this is a simple trick.
02:13If x is a number
02:15chosen randomly from set
02:173,5,7,9,11,13
02:21and y is chosen randomly from set
02:232,4,6,8,10,12
02:25what is the probability
02:27that x plus y is greater than
02:2950?
02:31Now,
02:33let's see.
02:35This is a set.
02:37This is a set.
02:39This is a set.
02:40This is a set.
02:41This is a set.
02:42This is a set.
02:43This is a set.
02:44So, probability
02:45that x plus y is greater than 15.
02:47Wait a minute.
02:48First,
02:49how will we make total outcome?
02:50How many members?
02:511,2,3,4,5,6.
02:531,2,3,4,5,6.
02:541,2,3,4,5,6,5,7,13
02:56This is a set.
02:57This will come.
02:58Now,
02:59let's see.
03:00In 3,
03:01if you have no number plus
03:0215 is greater than 15.
03:03In 3,
03:04if you have 12 pluses,
03:05then 15 is equal.
03:07In 4,6,8,
03:08it will not be equal to 10.
03:09Now, let's see.
03:10It's a simple trick.
03:115 plus 10 is 30.
03:13It's 15.
03:14Okay?
03:15It's not equal to greater.
03:16So, in 5,
03:17let's 12 pluses.
03:18Of course, greater will come.
03:20In 7,
03:237 plus 8,
03:2515.
03:26No.
03:27Yes.
03:287 plus 10
03:29and 7 plus 12,
03:3015.
03:31Two numbers here.
03:327 plus 8,
03:36how much?
03:3715.
03:39Now,
03:40in 9,
03:419 plus 6,
03:4215.
03:43How much?
03:44When 9,
03:458,
03:4610,
03:47or 12,
03:48if you have 4 pluses,
03:49then 15.
03:50But in 11,
03:516,
03:528,
03:5310,
03:5412,
03:55then 4.
03:56In 13,
03:57you have no number pluses.
03:584,
03:596,
04:008,
04:0110,
04:0212.
04:03In 13,
04:04you have no number pluses.
04:054,
04:066,
04:078,
04:0810,
04:0912,
04:1012,
04:1112,
04:1212,
04:1312,
04:1412,
04:1512,
04:1612,
04:1712,
04:1812,
04:1912,
04:2012,
04:2112,
04:2212,
04:2312,
04:2412,
04:2512,
04:2612,
04:2713,
04:2813,
04:2914,
04:3013,
04:3114,
04:3214,
04:3314,
04:3415,
04:3515,
04:3615,
04:3715,
04:3815,
04:3915,
04:4015,
04:4115,
04:4215,
04:4315,
04:4415,
04:4515,
04:46I mean, we have 4, 4, 4, and 4.
04:48And then, we have 4 plus 5, 9.
04:50But, but, but,
04:52now, there is a very bad change.
04:54What is the bad change?
04:56What is the bad change?
04:58Now, we have 3 to speak.
05:00And 3 and 3 are black.
05:02So, first, see, black is how many?
05:045.
05:06So, there will be 5 combinations.
05:08And then,
05:10the total number of points.
05:124, 5,
05:149.
05:16That means,
05:189 combinations.
05:22Now, very easy.
05:24Look, combination 3
05:26which is our formula
05:28that is
05:30n, n-1,
05:32n-2,
05:34upon 6.
05:36So, n
05:38will come up? 5 will come up?
05:405 will come up?
05:429 will come up.
05:445,
05:455-1,
05:464,
05:475-2,
05:483,
05:49upon 6.
05:506,
05:516,
05:526,
05:536.
05:546,
05:556,
05:566,
05:576.
05:586,
05:596.
06:00I don't know what the answer is.
06:02This one is cut.
06:04This one is cut.
06:06It's cut.
06:08This one is cut, this one is cut.
06:10This one is cut.
06:12Three twos are six.
06:14Six sevens are fourtato.
06:16Five upon fourtato.
06:18This one is cut.
06:20And that's your law.
06:22The answer is cut.
06:24The bag of four white and five black balls are.
06:26We would have to select 3 balls and 3 balls.
06:283-1 and 3-3-1
06:30So, the first thing is that
06:322 combinations are
06:34There are only black balls
06:36Black balls are only 5
06:38So, I have 5-5
06:40Because there are 3-3
06:42And there is a total
06:44Total is 4-5
06:469 balls
06:48Now, we have 3-3
06:50Black balls are only 3-3
06:52So, there will be 9 combinations
06:54Combination 3
06:56N, N-1
06:58N-2
07:16Cut, cut and cut
07:18Cut and cut
07:20Now, what is the question?
07:22From a bag containing
07:24and 5 black balls, men draw 3 at random, what is the chance of drawing 2 black ball and 1 white?
07:31I mean, all of them are not black balls, but who has 2 white balls and 1 black ball?
07:37So, now, what kind of a story?
07:40Very, very interesting situation.
07:431 white, 2 black balls.
07:46We have to select the 3 balls and 2 white balls.
07:50You see, white balls are 4, black balls are 5.
07:53Now, we have to select 5 black balls.
07:55We have to select 2.
07:57We have to select 5 combinations.
08:00But, we have to select 3.
08:02We have to select 1.
08:04And, white total is 4.
08:06We have to select 4 combinations.
08:08Under the formula, this is 9 combinations.
08:10We have to select 3 combinations.
08:12Now, what will we do?
08:14We have to select 4 combinations.
08:16If you have to select 1, then it will be very easy.
08:19Then, 4 will be added.
08:21If you have to select 2, then we will select 2.
08:24Then, the formula is called 2.
08:25N into N minus 1 upon 2.
08:26N is 5.
08:275 minus N is 4.
08:295 minus N is 4.
08:30Upon 2.
08:329 combinations 3 or upon 2.
08:349 combinations 3 or upon 2.
08:366 or 9.
08:388 or 7.
08:409 combinations 4 or 7.
08:41Now, the cut-up scale will be cut?
08:43Yes, of course.
08:45The 4 is cut.
08:464 will be cut.
08:482 is cut and 2 will be cut.
08:51And, the error will be cut.
08:53Look, what a 3 is cut.
08:55And then, the error will be cut.
08:57This is 3.
08:58The error will be cut.
08:59And then, the error will be 4.
09:01We will solve all the problems, but there is a simple calculation.
09:06There is no problem.
09:08Look, 4-4 is also cut.
09:10And on the top, 5 or 2 is multiplied.
09:16Look.
09:18And the bottom, what will happen?
09:207 or 3 is multiplied.
09:2210 upon 21 is done.
09:24But we will solve all the problems.
09:26This is a good one.
09:28Group consists of 4 boys and 3 girls.
09:313 persons are selected at random.
09:34Find the probability that all 3 selected are boys.
09:39All 3 selected are boys.
09:43So, good, Salih.
09:444 girls and 3 girls.
09:46And we need to select 3 persons.
09:49So, we need to select 3-3 girls.
09:51So, this is the problem.
09:53So, what you need is the girls.
09:56How many girls are?
09:574.
09:58So, it will be 4.
09:594 combinations of girls.
10:00And below is total, boys and girls.
10:02How many girls are 4?
10:04How many girls are 4?
10:054 plus 3?
10:067.
10:07So, it will be 7.
10:09Solve the answer.
10:10So, you can tell me the answer.
10:12I will tell you.
10:13I will tell you.
10:144 upon 35.
10:15Because 4 combinations of 3.
10:18So, if this is one for 3.
10:19Or on the bottom is 1.
10:20Or on the bottom is 1.
10:21That is part of the answer.
10:224 is always 4.
10:24And in that upper half,
10:25seven combination of 3 gives 35,
10:26which is a very popular result.
10:28Seven combination of 3 is so much money.
10:31So, boys, tell me.
10:33So, let me tell you, this is going to be a lot of people to be aware of it.
10:37So, I'm going to ask you seven nominations.
10:39It's going to be 35.
10:40So, we're talking about three events.
10:42We're talking about one course A, one course B, and one course C.
10:48So, we're talking about inclusive or exclusive.
10:52We're talking about previously animals' birds.
10:58So, what are they? Exclusive.
11:00So, those who arefree will be the animals and animals' birds.
11:04But here are three courses as inclusive events.
11:08We're taking three courses, A, B, C.
11:11Some children can study A, B and C.
11:15Look at this is an important part of A and B.
11:18For this, A and B are both of them.
11:20These are the two B and C.
11:23And these are the two C and A.
11:25But, this is a small portion.
11:28which is A, B, C is 3.
11:30So, sometimes a question will be asked
11:33that probability A, B, C is reading the probability of reading the book.
11:36So, we can write this way
11:38A union B union C
11:40or A and B and C.
11:42So, this is a formula.
11:44Probability of A plus probability of B plus probability of C.
11:48It's simple.
11:50A probability of B and C.
11:52Then minus what is the difference?
11:54Intersection B?
11:56Minus A intersection C
11:58and minus B intersection C.
12:00And then again, what do we do in the formulae?
12:02This part.
12:04Intersection B intersection C.
12:06So, the question in the paper
12:08was that A probability is 0.8
12:10B is 0.7
12:12C is 0.6
12:14and this is 0.4
12:16and this is 0.3
12:18and this is 0.2
12:20and this is 0.1
12:22So, this is the question
12:24which means the value of the value
12:26value is 0.4
12:28and that is 0.5
12:30and this is 0.5
12:32which means 0.5
12:33and 0.5
12:34and 0.5
12:36and 0.5
12:38So,
12:400.1
12:411.1
12:441.1
12:46Okay?
12:48and
12:50we will also have kindly collect this
12:52Here is 0.45
12:54and here is 0.35
12:56Okay?
12:57So we will just solve it in the formula
12:58We will keep the formula
12:59And I will see the answer
13:00Here is the formula
13:02This is the formula
13:06This is the formula
13:08So, what do you think about the formula?
13:12A, B, and C?
13:15This is the same way that A union B union C
13:19It is the same way that A is 700, B is 600, C is 500
13:25There are 200 who have A and B and C
13:28There are 300 who have A and C
13:30There are 300 who have A and C
13:32There are 300 who have A and C
13:34There are 300 who have A and C
13:36So, A plus B plus C minus A intersection B minus A intersection C
13:40Minus B intersection C plus A intersection B intersection
13:44Another great question
13:46There are 6 true-false questions on the test
13:50In how many different ends can the 6 questions be answered?
13:566 questions, how are true and false?
14:00And how can we answer 6 questions?
14:04There are a little bit of use
14:06When we were talking about coin problems,
14:10How many of us are in the coin?
14:12Head or tail?
14:14And this is the same thing?
14:16True-false will be true or false
14:18So, for head and tail, we have put a general formula to give power and
14:22To give power and
14:24To give power and
14:26To give power and
14:28To give power and
14:30To give power and
14:32What is true-false questions?
14:346 questions
14:36To give power, 6
14:38To give power, 6
14:40To give power, 6
14:41Carpenter has 10 Patterns of Chair and 8 Patterns of Table
14:50In how many ways can he make a pair of table and chair?
14:55So, see, there are 10 types of chair and 8 types of chair
15:02And which pair are you talking about? Table and chair
15:06So, it's very easy to take a pair of chair
15:08Chair is 10, table is 8, and multiply it with 10, 8 is 80
15:15So, this is a very important concept of probability
15:19This is a probability
15:21Let's see
15:23One class is 15 boys and 5 girls
15:26We choose one student to choose one
15:30Randomly
15:32How many chances are that the student is a boy?
15:36How many chances are that the student is a boy?
15:40Probability is a simple concept
15:43Because this concept is not clear for people
15:46So, this is the basic concept of probability
15:49Reviewing
15:50This is a very common example
15:52How many boys are?
15:5415
15:55And how many students are?
15:5715 plus 5
15:5920
16:00So, boy's probability is 15 upon 20
16:03Or 3 upon 4
16:04What is the probability of boy's probability?
16:07Note down, kids
16:08But if you ask, boy's probability is not an opportunity
16:10But if you ask, boy's not an opportunity
16:12Boy's probability is not an opportunity
16:14Complimentary
16:16It's always big
16:18So, the probability of an opportunity
16:20What will we do?
16:21The probability of an opportunity
16:22What will we do?
16:23In 1
16:24In 1
16:25In 1
16:26In 1
16:27In 1
16:28In 1
16:29In 1
16:30In 1
16:31In 1
16:32In 1
16:33In 1
16:34In 1
16:35In 1
16:36In 1
16:37In 1
16:38In 2
16:39Of
16:40In 1
16:41In 1
16:42In 1
16:43In 1
16:44In 1
16:45In 1
16:46In percentage, the sum is 100, and the probability is 1, and the fraction is 1.
16:55In fraction, the value is 1.
16:58For example, if you spend one-third money for clothing or one-fourth food,
17:05we spend one upon three and one upon four minus.
17:09This is 3 wide wall.
17:14It's 5 black balls.
17:17And what is the probability of making a wide ball?
17:22What is the probability of making a wide ball?
17:26So, I'm just talking about that.
17:30Overlake.
17:31It will come down, totally.
17:345 black.
17:373 plus 5.
17:413 upon 8 or 0.375.
17:44This is the option.
17:46This will be your answer.
17:48Black question is 5 upon 8.
17:515 upon 8.
17:52Now, in probability, there are many types of questions.
17:55There are many types of questions.
17:58There are many types of questions.
17:59The probability that
18:00Rehan will be able to solve a certain problem.
18:04Who knows?
18:05Rehan.
18:06Who knows?
18:07It's 5 by 5.
18:081 by 5.
18:09So, Rehan.
18:10What is the probability of solving this problem?
18:121 by 5.
18:13So, Rehan.
18:14How much chance of solving this problem?
18:151 by 5.
18:16And further, that Shweb will be able to solve this 1 by 4.
18:22Shweb's solving 1 by 4 is 1 by 4.
18:25If both boys work separately on the problem, the probability that both will solve.
18:32It's a very strange thing.
18:34Rehan's solving 1 by 5 is 1 by 5.
18:37Let's go.
18:38Shweb's 1 by 4 is 1 by 4.
18:40Now, if both solve separately on the problem, the chance will be able to solve it.
18:44Look, it's a very long method.
18:47So, we'll use a trick.
18:48What trick will happen?
18:50Both are all individuals.
18:52Rehan's 1 by 5 is 1 by 5.
18:54So, Shweb's 1 by 4 is 1 by 4.
18:57If Shweb's 1 by 4 is 1 by 4, then Rehan's 1 by 4 is 1 by 4.
18:59So, when we have 2 different events, it's a big difference.
19:02It's always a multiplication.
19:04So, 1 by 4 is 1 by 4 is 1 by 5.
19:08And when we multiply them, the answer is 1 upon 20.
19:13My brother, everybody in a room shakes hands with everybody else.
19:19What's the problem?
19:20The total number of handshake is 66.
19:23The total number of handshake is 66.
19:25The total number of person in the room is...
19:28Now, the total number of handshake is 2 for handshake.
19:33And the total number of handshake is N into N minus 1 upon 2.
19:38How many handshakes are now?
19:4166.
19:42So dare, dare, dare
20:09Forst of course, we will put options
20:14here in 11, 12, 13, 14, 15
20:17The answer is 0
20:19If left, put 6 and 6
20:21at the same time, the answer will be 0
20:24If left and left, put 12
20:28If I put the 12, then
20:3112-11 upon 2
20:3412 to 12
20:36611 to 66
20:38So of course answer is what will happen
20:4012
20:41Now you will ask
20:42Is this quadratic factorization
20:44very difficult to do
20:46It will be more difficult to do
20:48Options
20:50Options
20:51Counting technique
20:53Topic is a lot of
20:55This way
20:56People are confused
20:58How do permutation
20:59I will ask
21:01But if you have to do it
21:03I will ask
21:05Permutation
21:06Combination
21:07If you have to find
21:09So
21:10system
21:11Number of ways
21:125 people
21:14How many people
21:16Do they have to sit in a circle
21:18And
21:205 people
21:22In a circle
21:23Do they have to sit in a circle
21:25In a circle
21:27In a circle
21:28So, how many number of rows are possible?
21:31So, dear, dear, dear, dear.
21:34If we're talking about number of rows,
21:38we're talking about the formula,
21:41we're talking about n's factorial.
21:44We're talking about 7-7 revision.
21:46We're talking about 5.
21:48Now, what's the factorial?
21:51You're talking about 5.
21:52You're talking about 5,
21:53and you're talking about 120.
21:57So, what's the formula for?
22:02The formula is n-1 vector.
22:075-1 is 4 vector.
22:10Which is 24.
22:13The formula is n-1 vector divided by 2.
22:18Solve.
22:20When we're talking about 5 persons,
22:23this answer is 12.
22:26Okay, boys.
22:27A very good question.
22:28If you have 7 friends,
22:30and if you have 7 friends,
22:31if you have a row,
22:33then you ask, sir,
22:34what is the problem?
22:35We're talking about n factorial,
22:37or 7 factorial.
22:39And 7 factorial is 5-0,
22:43and 4-0.
22:45We're talking about 9.
22:46We're talking about 9.
22:47We're talking about 9.
22:48We're talking about 9.
22:49Of course,
22:50we're talking about 9.
22:51But, boys,
22:52if we're talking about this question,
22:53in how many ways,
22:557 friends sit in a row,
22:59so that particular person is at center?
23:02So, where are we?
23:03Where are we?
23:04In the center.
23:06In the center.
23:07So,
23:08we're talking about 7 people
23:09and we're talking about this way.
23:10So,
23:11we're talking about 9.
23:12So,
23:13we're talking about 9.
23:14So,
23:15we're talking about 9.
23:16We're talking about 9.
23:17So,
23:18in the center.
23:19So,
23:20what will be the 4th seat?
23:21The center.
23:22Now,
23:23it said,
23:24my seat is in the center.
23:25How many seats have you?
23:27Go ahead and explain.
23:281,
23:292,
23:303,
23:313,
23:32and 5,
23:336,
23:34How many seats?
23:356.
23:36So,
23:37what will be the answer?
23:386 factorial.
23:39And,
23:406 factorial,
23:417.
23:42Why?
23:43That's why
23:44the center
23:45particular.
23:46They said,
23:47this place is my place.
23:48Now,
23:49I'll sit here.
23:50I'll sit here.
23:51I'll sit here.
23:52So,
23:53I'll sit here.
23:54My brother,
23:55I'll sit here.
23:56Then,
23:57the other people,
23:58are sitting here.
23:596 factorial,
24:007.
24:01Okay,
24:02children.
24:03We're talking about
24:04some properties.
24:06Some properties
24:07are for long.
24:08Some
24:09for long.
24:10Some
24:11for long.
24:12So,
24:13that's the point.
24:14What?
24:15What?
24:16What?
24:17What?
24:18What?
24:19What?
24:20What?
24:21How many?
24:22Each person
24:23is at either end.
24:26What?
24:27Either end.
24:28Either end.
24:29Either end.
24:30I can say,
24:31either end.
24:32What?
24:33I'll say,
24:34who?
24:35Who?
24:36Who?
24:37Who?
24:38Who?
24:39If he is sitting in this corner, how many places are left?
24:436.
24:446 factorial is 720.
24:46But one is not one.
24:48How many places are left?
24:50If he is sitting in this corner, then how many places are left?
24:556.
24:566 factorial.
24:58If he is sitting in the left corner, then 6 factorial is 720.
25:04If he is sitting in the right corner, then 6 factorial is 720.
25:09If he is plus, then what will he be?
25:141, 4, 4, 0.
25:178 factorial is 8.
25:208 into 7 into 6 into 5 into 4 into 3 into 2 into 1.
25:264, 0, 3, 2, 0.
25:289 factorial is 3, 6, 2, 8, 0.
25:325 factorial is 9.
25:35Now tell us, what is wrong with this?
25:3810.
25:39This should be an easy way.
25:40This will not be full!
25:411, 2, 0.
25:44The factorial has started.
25:46Because it is factorial, though it is no problem.
25:48So, if 10 is not a problem, then it will be a problem.
25:50This change will not be afraid of this.
25:53We are going to have 9,000.
25:55This is a problem.
25:57that Keraji
25:59from Hedraabad
26:00is three number of ways
26:043 ways
26:04Hedraabad
26:07from Lahore
26:07is four ways
26:10and Lahore
26:12from Islamabad
26:13is five ways
26:14total how many ways
26:17Keraji
26:18from Islamabad
26:19again
26:20Keraji
26:22Keraji
26:22from Hedraabad
26:22is three
26:23and
26:24Hedraabad
26:25from Lahore
26:26is four
26:27and
26:28Lahore
26:28from Islamabad
26:29is five
26:30so Keraji
26:32from Islamabad
26:33is how many
26:34number of ways
26:35are possible?
26:35this is a very easy
26:38multiplication
26:39Keraji
26:41to Hedraabad
26:43root one
26:45root two
26:47root three
26:49Hedraabad
26:50to Lahore
26:51is four
26:52one
26:53two
26:53three
26:53four
26:54like this
26:54then
26:55so Keraji
26:56to Hedraabad
26:57root one
26:58to Keraji
26:59to Lahore
27:00to
27:01Lahore
27:02to
27:03Keraji
27:04to
27:05Keraji
27:06to Lahore
27:07to
27:08Keraji
27:09to Lahore
27:1012
27:1112
27:12to
27:13Hedraabad
27:14to
27:15Hedraabad
27:1612
27:17to
27:18Hedra
27:19to
27:2012
27:21to
27:22Keraji
27:23to
27:24Lahore
27:25to
27:26Hedra
27:27to
27:28Hedra
27:29to
27:30Hedra
27:31to
27:32Hedra
27:33to
27:34Hedra
27:35to
27:363
27:374
27:38to
27:39Hedra
27:4012
27:41to
27:42Hedra
27:43to
27:44Hedra
27:45to
27:47Hedra
27:48to
27:49Hedra
27:50to
27:51Hedra
27:52to
27:53Hedra
27:54and
27:55combination
27:56Batao
27:57N
27:58to
27:59bade
28:00to
28:01combination
28:03to
28:04equal
28:05to
28:06to
28:08or
28:09N
28:10to
28:11n
28:12to
28:13in
28:14do
28:15plus
28:1610
28:17or
28:185
28:19to
28:20Now, if you don't like this, you can get 10 and 5, so I'm going to provide a lot of money.
28:27This is a very dangerous formula.
28:31But in paper, we need to remember the formula.
28:38What is the formula?
28:40N minus 1 combination R plus N minus 1 combination R minus 1.
28:49What is the formula?
28:52This is N combination R to R.
28:55So, the formula is the number of questions.
28:59So, if we have the question of the 15 combination 11 plus 15 combination 10,
29:04which is the number of questions?
29:06So, let's look at the formula.
29:08The formula is N minus 1.
29:11The formula is N minus 1.
29:13And then, the formula is N minus 1.
29:15The formula is N minus 1.
29:16I mean, this value is a small one.
29:19So, the result is n combination of r.
29:23What is our formula valid?
29:25And what is n?
29:26What is r?
29:27So, look at it.
29:29Look at it.
29:30Look at it.
29:32The value of n-1 is 15.
29:34So, n is 16.
29:36And r is 11.
29:38Yeah.
29:39n-1 combination of r.
29:41I mean, it's 15 combination of r.
29:44Plus, it's 15 combination of r.
29:47And what is the final answer?
29:49n combination of r.
29:51So, n is 16.
29:53And r is 11.
29:55So, it's 16 combination of 11.
30:00And this is the answer.
30:02This is the only paper.
30:04The total number of prices is 20.
30:07How many?
30:0820.
30:09And we have 20.
30:1020.
30:1120.
30:12Well, the student is total number of prices.
30:15Can you click the link?
30:17Number of students is 20.
30:19And in 20 students, we have prices distributed.
30:22Which prices are?
30:23First price.
30:24Second price.
30:25Third price.
30:26Third price.
30:27the number of ways my prices distribute what's the name number of ways my prices
30:34wording about the first price second price I think first price really getting
30:43candidate on your previous
30:45yes
30:47yes
30:49up just a first time
30:51second time
30:53now
30:55the second year
30:57and
30:59in
31:01the job
31:03attitude test
31:05concept
31:07number of student
31:0920
31:11Physics, Chemistry, Math, 3 subjects.
31:15So, my brother, how many number of ways do you have to distribute?
31:22How many students do you have to distribute?
31:25And in 20 students, you have to give a prize in Physics, Chemistry, Math.
31:32How many number of ways do you have to distribute?
31:35What time do you have to do?
31:37How many number of ways do you have to distribute?
31:4220. Chemistry?
31:4420.
31:4520.
31:46Oh, brother, who can win in Physics, can win in Chemistry?
31:51No.
31:52It's a different thing.
31:53The one who has the first prize, is the second prize.
31:56The one who has the first prize, is the second prize.
31:58The one who has the first prize, is the third prize.
32:00But the one who wins in Physics, can win in Chemistry?
32:03You can give it yourself.
32:04You can give it yourself.
32:05You can give it yourself.
32:06And the one who wins in Math.
32:08So, the answer will be 20 into 20 into 20 into 20.
32:12How many different arrangements can be made by using all the letters of the word Kajol?
32:19Look.
32:20Where L, E always remain together.
32:24Look at how many letters in Kajol are.
32:26So, if you have 6, then we should take 6 to 6, but in the case of the突ot.
32:29But, there is a twist.
32:30There is a twist.
32:31Where you are, that L and E, we will just consider one letter.
32:34So, if we consider L and E to one letter, then how many letters are left?
32:381, 2, 3, 4, and 2?
32:401.
32:414 and 1, 5 letters.
32:435 is an important factor.
32:45But, but, but, but, but, what is this?
32:48What is this?
32:49That is, L is there and either.
32:50Either L is there and either.
32:51So, this means that 5 of the factorials multiply 5.
32:55So, this means that 5 of the factorials multiply 2.
32:58How much 5, how much 5 is?
32:595 into 4 into 3 into 2 into 1, 120.
33:01So, multiply 2 from 2 into 40.
33:03So, this means that it is the answer.
33:05Okay, this means a big topic is probability.
33:08Now, if you don't get to probability for this topic,
33:11then you can get the concept of this.
33:14Like the number is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, okay?
33:19Now, this is the number.
33:21You are saying the probability.
33:24Odd number comes.
33:26First, we will choose number 1 to 10,
33:28we will choose tickets and let's suppose.
33:30So, odd number comes from probability.
33:32The last probability comes from probability.
33:34Probability comes from possibility, okay?
33:37Maybe.
33:38Maybe.
33:39Maybe.
33:40Maybe.
33:41But, what number comes from probability?
33:43Well, 1, 3, 5, 7 or 9.
33:46How many odd numbers are there?
33:485, 10, so.
33:50Odd number comes from chance.
33:525 upon 10.
33:54Okay.
33:56Even like, 5 upon 10 is a half.
34:00Okay, yeah, half.
34:02We are getting smaller than probability.
34:05We are getting smaller than probability.
34:07Probability is 1, or 1- 1, or 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 2- 1- 2- 1- 1- 1- 1- 2- 1- 2- 3- 1- 1- 2- 1- 1- 1- 1- 2- 1- 1- 2- 1- 1- 1- 1- 1- 1- 1- 2- 1- 2- 1- 1- 1- 1- 1- 2- 1- 1- 1- 1- 2- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1- 1-
34:37so we have positive numbers which we have in our own way.
34:38We have 4, 2, and 6, 2, and 3, and 8, 2, and 4, and 9, 3, and 10, 2, and 5.
34:47So this is 5.
34:495 upon 10.
34:52Now, my brother,
34:55give me a question today, either odd or even number.
34:59So, either odd, when it comes to either,
35:03odd number plus even number.
35:05So, what do we do?
35:06Odd number also 5.
35:08Even also 5.
35:09I put 5 plus 5.
35:11We will always divide by the total.
35:14So, that's 10.
35:16What is 10 upon 10?
35:17It's 1.
35:18The probability is 1.
35:19Either even or odd.
35:21If you have neither even nor odd,
35:25then what will happen?
35:27Well, well, well.
35:29Neither even nor odd.
35:31So, brother,
35:33if you have no answer,
35:34no even or odd.
35:36Number even or odd?
35:37It's true.
35:38So, neither even nor odd.
35:40Whenever we ask questions,
35:42it's understood.
35:43What is your answer?
35:44What is your answer?
35:45It's 0.
35:46The probability is 0.
35:47Now, one big big thing is vector.
35:50What is vector?
35:51What is vector?
35:52What is vector?
35:53It's vector vector vector.
35:54It's vector vector vector.
35:55It's vector vector vector vector вдруг Cause.
35:56It's vector vector.
35:57I
36:06nearly regretted that due to inference.
36:09We gotta forget about multiple points.
36:11What is vector vector vector vector cách?
36:12I have 9 vectorials. I have 362, 880.
36:15Why did you write 10 vectorials?
36:18What do you think?
36:19What is 9 vectorials?
36:21Which is 9 vectorials?
36:23Which is 10?
36:24What is this?
36:26What is this?
36:27What is this?
36:29This is 10 vectorials.
36:32This is the concept.
36:34Who is this?
36:36Prop A.P.L.T.
36:37In the aptitude test,
36:39I have some different teachers.
36:42Some teachers have many legends.
36:45These are very good concepts.
36:48But all of these are.
36:50Some of these concepts don't exist.
36:53The most important thing is Prop A.P.L.T.
36:57What is this?
37:00In English Prop?
37:02If you look at something,
37:04There are some chance of happening.
37:07What happens?
37:08What happens?
37:09What happens?
37:10What happens?
37:11If you are a struggle,
37:1215 papers are passed.
37:14Total papers are 20.
37:17So, the probability of passing of passing
37:19is how much?
37:2015 upon 20.
37:21This is how passed.
37:23So, basically,
37:25we call the probability of passing
37:28that successful attempt
37:30divided by total attempt.
37:32What should it be?
37:33Probability.
37:34What should it be?
37:35Probability.
37:36What should it be?
37:3720 papers.
37:38How many papers have passed?
37:4015.
37:41So, the probability of passing is 15 upon 20.
37:43Can this be cut from 5KW?
37:463 upon 4.
37:48And 3 divided by 4.
37:50.75.
37:51Now, probability maximum
37:54is not enough.
37:55How can the probability maximum
37:57be done?
37:58Look.
37:59The percentage maximum 100
38:00is not enough.
38:02There is a probability maximum value
38:03to be 1.
38:04Probability is not enough.
38:06But the quantity is 0.
38:07As with the minimum value,
38:08it is not enough.
38:09It is 0.
38:10It is 0.
38:11It is 0.
38:12If it is 20 to 20 paper
38:13will fail,
38:14so probability is 0.
38:15If 20 paper will pass
38:16then 20 upon 20.
38:17It is 30 upon 20.
38:19How much probability is happening at least like 3 times?
38:221 ket dizer to, i mean maximum, i mean 100 percent
38:27Pass these is what probability is
38:29in this case here project
38:31How much would it be?
38:32.75
38:34We wrote place to name A
38:37звучание
38:41we also have to
38:44child 1987
38:46So, it doesn't happen to us.
38:48So, it doesn't happen to us.
38:50So, it doesn't happen to us.
38:52So, the probability doesn't happen to us.
38:54What do we do?
38:560.75?
38:58How much do we do?
39:000.25.
39:02So, the probability doesn't happen to us.
39:040.25.
39:06It's simple.
39:08Now, let's talk about this.
39:10Let's talk about dice.
39:12Let's talk about dice.
39:14How much do we do?
39:166.
39:181, 2, 3, 4, 5, 6.
39:221, 2, 3, 4, 5, 6.
39:24So, in the case of dice, how much do we do?
39:266.
39:28Total events how much do we do?
39:306.
39:32So, the question is,
39:34if we roll out the dice,
39:36then tell us the probability.
39:38The probability is the prime number.
39:40The probability is the prime number.
39:42The probability is the prime number.
39:442.5.
39:462.5.
39:483.5.
39:502 is a prime number, 3 is a prime number and 5 is a prime number.
39:56How many prime numbers are in total? 3.
39:58Remember that 1 is a prime or composite.
40:03So, we are asking if the prime number is 3 upon 6.
40:083 upon 6 means that half, half, then it is 0.5.
40:13Okay, 0.5.
40:15And if we say that the prime number is not probability,
40:21then one way, I will 0.5 minus.
40:24Now, we call it composite number.
40:28What is composite number?
40:30We call it composite number.
40:35We call it composite number,
40:37which means that we can divide.
40:40Who is 4 and 6?
40:43Which is this.
40:454 or 6.
40:48So, if we talk about composite number,
40:51which we talk about?
40:53Composite number.
40:55Composite number is 4 and what is 6?
40:58Composite number is 4 and what is 6?
41:00Composite number is 4 and what is 6?
41:02Composite number is 2 upon 6.
41:04Total event,
41:05we have single dice,
41:06we have single dice,
41:07we have six of them.
41:08Six of them.
41:09Six of them.
41:10This answer is 2 upon 6.
41:122 upon 6,
41:13what should we say?
41:141 upon 3,
41:15or point 3.
41:16Here we have no doubt.
41:17Exactly.
41:18The number 1 would be at the table.
41:26The number 2 will come by name for the verse better.
41:306.
41:32The number 1 is a nightmare.
41:34See your number 1 is a nightmare.
41:36Either our number 1 is not known.
41:38so how many words are possible?
41:40How many letters are?
41:426.
41:436 is a factorial.
41:45Is there any letters repeat?
41:47A is a repeat.
41:48How many letters repeat?
41:503 times.
41:51So it will be 3 times.
41:53Is there any other repeat?
41:553 times.
41:572 times.
41:596 into 5 into 4 into 3 into 2.
42:03So it will be 6 into 2.
42:066 and 6 together, they will die.
42:102 and 2 together, they will die.
42:14They will die.
42:15They will die.
42:16They will die.
42:17What else?
42:185 into 4 into 3.
42:2060.
42:22This is the total possibility.
42:25If you can make it, it will be 60.
42:29Let's go.
42:30If it happens to be together.
42:33Not together.
42:35two ends together.
42:362 ends together.
42:37So we can make them together.
42:392 ends together.
42:402 ends together.
42:412 ends together.
42:42How many letters are?
42:431B and 3A.
42:44Now look at this.
42:452 ends together.
42:46We have total letters.
42:475.
42:48Why?
42:49Why?
42:502 ends together.
42:51To be considered 2 ends.
42:522 ends.
42:532 ends.
42:542 ends.
42:552 ends.
42:562 ends.
42:57So, this is 5.
42:581, 2, 3, and 2 n.
43:00If the answer is together.
43:02So, the answer is 5.
43:04And the answer is divided by 3.
43:08Now, the answer is 3.
43:12So, 5! divided by 3.
43:15Of course, 5 into 4 into 3.
43:18Cancel the answer is 20.
43:21The answer is 20 when the answer is together.
43:25To end, not together.
43:27So, what do we do?
43:28How many total events are?
43:2960.
43:30And end together, 20.
43:32In 60, 20 minus.
43:34The answer is 40.
43:35Very simple.
43:36So, the answer is very good.
43:38Slip is picked out of 8 slips.
43:44Because we don't have a slip.
43:46Total is 8 slips.
43:48Number from 1 to 8.
43:50Then the probability to get number 4 is.
43:53This whole paper is very simple.
43:55How many total slips are?
43:578.
43:58And from 1 to 8.
44:01We have got a slip on number 4.
44:04So, the probability of 4 is coming.
44:07So, the probability of 4 is coming.
44:09So, the probability of 1 is coming.
44:11So, the probability of 1 is coming.
44:131 upon 8.
44:14This is 4 is coming.
44:16If there is no question.
44:18So, the answer is 1 upon 8.
44:201 upon 8.
44:21So, the answer is 7.
44:234 persons are chosen at random from group containing 3 men, 2 women and 4 children.
44:30What is the chance that exactly 2 of them will be children?
44:33So, the answer is how many children will be children?
44:34What is the chance that 2 children will be children?
44:38How many people will be children?
44:403 men, 2 women and 4 children?
44:42So, the answer is that we have total 4 people.
44:45I mean, nine combinations, four people will be total outcome.
44:48The outcome is 9, 4.
44:49The outcome is total outcome.
44:50Total outcome.
44:513 men, 2 women, 4 children.
44:54So, men are 2.
44:55And more children, 4 children will be 4.
44:56And the rest of the children need 4 combinations of 4 combinations of 2.
45:01The men and women need 5.
45:03And we need 2.
45:05So, we need 5 combinations of 2.
45:064 combinations of 2 is 6.
45:085 combinations of 2 is 10.
45:10So, 6, 10.
45:12This will cut.
45:13From the table of 6.
45:15So, it will be 10 upon 21.
45:17Which is easier.
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