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00:00Password's question is
00:02The box contains two white balls, three black balls and four red balls
00:09The number of ways in which three balls can be drawn from the box
00:16so that at least one of the ball is black
00:20In the box there are two white balls, three black balls and four blue balls
00:25Now select the number of ways in which one is black
00:31and one is black
00:33and one is black
00:38So what do you think?
00:40One is black, two white balls, three black balls and four red balls
00:51One ball is black, if there is no condition
00:54So if there are nine balls, then we need to select the number of balls
00:59Three balls
01:01Box contains two white, three black and four red
01:04So the number of ways in which three balls can be drawn from the box
01:08If there are only three balls from the box, then it's three balls
01:11So what do you think?
01:13The number of ways in which three balls can be drawn from the box
01:15So what do you think?
01:16What do you think?
01:17One of them is black
01:18One of them is black
01:20So this is an easy trick
01:22Very awesome trick
01:23What do you think?
01:24What do you think?
01:25What do you think?
01:26What do you think?
01:27What do you think?
01:28What do you think?
01:29Three black is
01:30So there is no black
01:31So there is no black
01:32So there is no black
01:33So what do you think?
01:34What do you think?
01:35How do you think?
01:36What do you think?
01:37Four red balls
01:38Or two white
01:39Two white
01:40And four red balls
01:41How do you think?
01:42Six
01:43So there is no black ball
01:44So there is no black ball
01:45Six combination
01:46Three multiply by
01:47Three combination
01:48Zero
01:49So black ball
01:50Do not have any chance
01:5120
01:52And total chance
01:5384
01:54So black ball
01:55What do you think?
01:5684 minus
01:5720
01:58So the answer will be
01:5964
02:00It is very easy
02:01Whenever you think
02:02No blue ball
02:04No white ball
02:05No white ball
02:06No other things
02:07It is the most easy
02:08That you think
02:09No black ball
02:10And total 84
02:12This is minus
02:13But good
02:14The box contains
02:15Two white balls
02:16Three black balls
02:17And four red balls
02:18The number of ways
02:19In which two
02:20Balls can be drawn
02:22From the box
02:23So that at least
02:24One of the ball
02:25Is white
02:26No white ball
02:27No white ball
02:28So now go
02:31If there is no
02:32Condition
02:33Then simple
02:349 combination
02:35Theory is 84
02:36But now
02:37What are you saying?
02:38That two balls
02:39We have to select
02:40One white ball
02:42So now
02:43We will see
02:44No white ball
02:45Which condition
02:46No white ball
02:47No white ball
02:48Okay?
02:49So
02:5084
02:51So
02:5284
02:53When
02:54We have to select
02:55Three balls
02:56Now
02:57No white ball
02:58So total
02:59Two white balls
03:00We have to select
03:01Two combinations
03:02We have to select
03:03How much
03:04To select
03:05Three balls
03:06Nine
03:07Two minus
03:08Then
03:09Seven
03:10Three black
03:11And
03:12Four red
03:13So
03:14Seven combinations
03:15Seven combinations
03:16Three
03:17Thirty five
03:18Eight
03:19Eight
03:20Four
03:21Thirty
03:22Nine
03:23One
03:24Five
03:25Five
03:26All
03:29Three
03:30Four
03:31Three
03:32Four
03:33red
03:34The number of ways
03:35in which
03:36four
03:37Balls
03:38Can be drawn
03:39from the box
03:40so that at least one of the ball is red.
03:44We have to select 4 balls when there are 2 white, 3 black and 4 red.
03:51So at least red.
03:53If there is no condition, 9 combination 3 is 84.
03:56Now we are talking about no red ball.
03:59Okay?
04:00No red ball.
04:02So my brother, red ball is 4.
04:05And in 4 we have no one.
04:07So 4 combination is 0.
04:09Combination is 0 and 1.
04:11And now we have to select 5.
04:15We have to select 3 black and 2 red.
04:18We have to select 3.
04:195 combination 3 is 10.
04:21Now we have to select 84.
04:25A very good question.
04:27The number of different 4-digit numbers that can be formed.
04:33With the digit 2,3,4,5,7.
04:38Using each digit on the mouse.
04:41Now see.
04:42How many digits are?
04:442,3,4,5,7.
04:465 digits.
04:47Number of digit 5.
04:48We are making 4 digits of this.
04:50What are the digits of this?
04:52Unit, 10, 100 or 1000.
04:55So now see.
04:58Here, there are 5 numbers here.
05:01No number 5.
05:03But because there is no repeat.
05:04The number here is no.
05:05The number here is no.
05:06Here is no.
05:07There is no.
05:08Here, there are 4 numbers.
05:09And in 10 digits, there are 3 numbers.
05:11And in 10 digits, there are 3 numbers.
05:12And there are 2 numbers.
05:13Now, all of these numbers are multiplied.
05:15So, result will be 1.
05:17One to go.
05:18One to go.
05:19One to go.
05:20Two to go.
05:21Two to go.
05:22One to go.
05:23Two to go.
05:24Two to go.
05:25The other is this.
05:26The other is this.
05:27The other is this.
05:28Digit problem.
05:29In the problem.
05:30You get confused that permutation can be used in a combination, so I can use a combination.
05:35But with this type of problem, permutation can be very easy to use.
05:405 number and how much is happening? 4 digits.
05:43So, you use 5 permutation 4.
05:475 vectorial.
05:49What does permutation mean?
05:51The difference is 5 minus 4 is 1.
05:55So, 5 vectorial is 120,
05:58if the letters L, O, G, I, N, C are randomly arranged,
06:08to form a 5 letter word, what is probability that the result will be word logic?
06:16If there are 5 letters, then 5 vectorial will make it.
06:22Because it doesn't repeat in any letter name.
06:25L, O, G, I, C.
06:27Now, how much is the chance to become a logic?
06:30I mean, it's exactly the chance to be 1.
06:33So, 1 upon 5 vectorial.
06:355 vectorial means 5 into 4 into 3 into 2 into 1.
06:39So, 1 upon 120 is your answer.
06:41So, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4.
06:47And, what is the probability that a number selected and random from the set of numbers above will be the average of the set?
06:59So, 1, the first loss of the number is 1.
07:00So, 1th is my answer.
07:01Now, the first mistake of the number is the average.
07:03To multiply this dunno, the number is 30.
07:06Sub of the number is the number.
07:07So, the number is 30.
07:08So, 30 into 30, so, 10 divided by 3.
07:09So, average is 3.
07:10You are wondering how much the probability will come from average?
07:13So, average is 3, so, 4.
07:15Total number is 10.
07:17Total number is 10.
07:184 upon 10
07:19or 2 by 5 is over answer.
07:21Simple numbers here.
07:22This was given by 1, 1, 2, 3, 4, and 4.
07:27And what happened is the thing happened.
07:28The probability was that the number that we are looking at
07:32to go to average from above?
07:36To go to average from above to about 4.
07:38But if it was below,
07:40I would count 1 again and 2 again.
07:43If the letters L O G I N C are randomly arranged to form a five-letter word, what is the number of letters?
08:13If the letters are 5, it will be a vector.
08:23Because there is no letter in any letter.
08:26L O G I C.
08:28Now how much chance of the logic to form a one-letter word?
08:31The chance of this is 1.
08:341 upon 5 factorial.
08:365 factorial means 5 into 4 into 3 into 1.
08:401 upon 120 is the other.
08:42Circle above is divided into 8 sectors of equal area.
08:49What is the probability that spinner will land on an E1 number region in each of the 2 consecutive spin?
09:001 spinners wall.
09:02Now look at the region.
09:04This is odd, this is odd, this is odd, 5 is odd, 3, 3.
09:08E1 region is where?
09:10Here is 2, here is 2 and here is 4.
09:122 spinners have 2 balls.
09:14There is a lot of chance to win.
09:16There is a lot of probability that the two games will win at the E1 level.
09:21If it's a first ball,
09:22then Mr Ali would have to have a 3 by 8 chance to win at the E1 level.
09:27How much?
09:28No, it's just total 8-1.
09:31And even value of 4, 2, like 2.
09:343 by 8.
09:35If the second ball is done, then it's 3x80.
09:40But it's a little bit.
09:42Then it's 3x80.
09:44Why?
09:45I can't do that.
09:46I can't do that.
09:48I can't do that.
09:50The answer is 3x80.
09:539 upon 64.
09:55If the third ball is done, then it's 3x80.
09:58Because it's even.
10:00If it's odd, it's 5x80.
10:03The back contains two orange.
10:06Three purple and two blue balls.
10:10Two blue balls are drawn at random.
10:14What is probability that none of the ball drawn is blue?
10:21There are two orange balls.
10:24Three purple balls.
10:27And two blue balls.
10:29You say that you have two balls to select.
10:32But it's blue.
10:34Well, this means that
10:36You have two balls to select.
10:41Seven combinations of two.
10:44And
10:45Here we have two balls to select.
10:47So, if we have two blue balls to select.
10:48If we have blue balls to select, then how many balls to select?
10:505.
10:512 orange.
10:523 purple.
10:54So, we have two balls to select.
10:56We have two balls to select.
10:57So, the left will be 5x80.
10:59The right will be 5x2.
11:00And the right will be 7x2.
11:02The right is that
11:03Now, when we write the formula to this combination,
11:07So here will be 10 or 21.
11:10The answer will be 10 upon 21.
11:131.
11:14Good.
11:15In box there are 8 oranges, 7 purple and 6 green balls.
11:23One ball is drawn randomly.
11:26What is probability that it is neither orange nor green.
11:35Neither orange nor green.
11:37So this is not orange nor green.
11:39This is not purple.
11:42Neither orange nor green.
11:46Total ball is how many?
11:508, 7 and 6 is 21.
11:53And 7 upon 21 is how many?
11:561 by 3.
11:58This is easy because 1 ball is required.
12:02Whenever you need one ball, you don't use combination.
12:06Which one should we?
12:07Neither orange nor green.
12:11This one should purple.
12:13And total ball is how many?
12:157 upon 21 is 1 by 3.
12:171 by 3.
12:20Raffle tickets number consecutively from 1, 0, 1, 0, 350 are placed in a box.
12:28What is probability that the ticket selected at random will have a number with 100 digits of 2?
12:36How many?
12:53I don't have a number of 100 digits of 2.
12:59100 digits of 2 will be 200.
13:02How many will be 200?
13:04How many will be 100?
13:07100 upon 250.
13:10Is it cut from 50 tables?
13:12No.
13:13First, cut 0.
13:14Then cut from 5.
13:162 upon 5.
13:17That is your answer.
13:19If we solve these questions, we don't know how much it is.
13:23So, I will start a little bit.
13:25If a person purchased 15 of the 3,000 tickets.
13:31I bought a 50 ticket for 3,000.
13:34Sold in a rifle.
13:36That awards one prize.
13:40What is the probability that this person will not win?
13:43The probability that this person will not win.
13:46Now, see.
13:4815,3,000.
13:51It is cut from 15 to 30 tables.
13:551 upon 200 is the chance of winning.
13:58What will the chance of winning?
14:00Not winning.
14:02Let's minus 1 upon 200.
14:04What is the answer?
14:06199 upon 200.
14:091?
14:102,000.
14:111.
14:122,000.
14:132,000.
14:14It is a big question.
14:15What is the answer?
14:16If 3-digit integer is slatted at a random.
14:20From integer 100,3199.
14:21Inclusive.
14:22What is probability that the first digit and the last digit of integer are equal to one more than the middle digit?
14:35This is a unit digit, a 10 digit, a 100 digit, this is the first, this is the last and this is the middle.
14:43There are some situations like this, that the first digit and the last digit, what is the middle digit?
14:51For example, if you have 1212, you can have another number, you can have another number, you can have another number, you can have another number.
14:57Now you can say that it can be very much, but there is a condition, where do you need to take 100 from 199.
15:04100 from 199, how much is the total?
15:08100.
15:09And this is a digit in this situation, which means the middle number is small, and this is the first and the last one.
15:16So, it's one here, 108.
15:18It's one here, right?
15:20What will the answer go up?
15:22That's the answer, 1 upon 100.
15:24Now, see, this was a very sweet question.
15:26If 3-digit integer is selected at random from integer 100-0-199 in closer,
15:32what is probability that first digit and the last digit of integer are equal to one more than the middle digit?
15:381,5,10 and 1,5.
15:391,5.
15:401,5.
15:411,5.
15:421,5.
15:431,5.
15:441,5.
15:451,5.
15:461,5.
15:471,5.
15:481,5.
15:491,5.
15:501,5.
15:511,5.
15:521,5.
15:531,5.
15:541,5.
15:551,5.
15:561,5.
15:571,5.
15:581,5.
15:591,5.
16:011,5.
16:021,5.
16:03What is probability that, the lost coins have value more than 15?
16:061,5,10.
16:071,5.
16:081,5.
16:091,5.
16:101,5.
16:111,5.
16:12Then 5 is equal to 1, 10, and 20.
16:21I can say that it is equal to 1 and 5.
16:241 and 10, 1 and 20.
16:30This can also be equal to 5 and 10.
16:335 and 20.
16:37Or 10 and 20.
16:40So, the value of the coin is equal to 5.
16:46There are 3 possibilities in which the answer is less than 5.
16:51The probability of the value of the coin is equal to 5.
16:54It is equal to 25.
16:57One bag.
16:58The bag contains 25 cloth bags of which 15 are plastic bags and 10 are wooden bags.
17:05If 4 bags are taken from the bag at random,
17:08the probability that 2 are wooden and 2 are plastic.
17:11Now, the value is good.
17:14The plastic bag is 15.
17:16I will also have 2 slack.
17:18The wooden bag is 10.
17:19I will also have 2 slack.
17:20The total is 25 bags.
17:21So, the answer will be 10 combination 2 into 15 combination 2 divided by 25 combination 4.
17:28Any option.
17:29Any option.
17:30A bag contains 25 cloth bags of which 15 are plastic bags and 10 are wooden bags.
17:39If 4 bags are taken from the bag at random, find the probability that all are wooden.
17:45Now, we are talking about all the wooden bags.
17:48So, how many are wooden bags?
17:50How many are wooden bags?
17:51So, it is 10.
17:52I will have 4 wooden bags.
17:5410 combination 4.
17:55Now, how many are total bags?
17:5725.
17:58So, we will divide 10 combination 4 into 25 combination 4.
18:02So, the answer will be 1.
18:04Okay.
18:05Party of M persons sit at a round table.
18:08Find the probability of two specified individuals sitting next to each other.
18:14So, if you are in a close round table, if you are in a close round table,
18:18if you are in a close round table,
18:19the probability of two specified individuals is close to each other.
18:24So, if you are in a close round table,
18:262 upon M minus 1.
18:28Because they do something.
18:29They don't have M.
18:31So, M is 7.
18:33So, what I will do here?
18:35In a close round table, M is 7.
18:37So, I will put 7 in the formula.
18:392 upon 7 minus 1.
18:402 upon 6.
18:412 upon 6.
18:42So, I will put 7 in the formula.
18:43I will put 7 in the formula.
18:44I will put 7 in the formula.
18:458 in the formula.
18:469 in the formula.
18:47So, this is an important one.
18:48Okay.
18:49So, the bag contains 25 cloth bags.
18:5125 cloth bags.
18:5225 cloth bags.
18:5325 cloth bags.
18:5415 are plastic bags.
18:5615 plastic bags.
18:5715 plastic bags.
18:5810 are wooden bags.
19:00If 4 bags are taken from the bag and random find the probability that all 4 are plastic.
19:0925 cloth bags.
19:1025 cloth bags.
19:1115 plastic bags.
19:1210 bags.
19:13If we have 4 bags.
19:14If we have 4 bags.
19:15Then, the probability is that 4 by 4 are plastic.
19:18Now, let's see.
19:19Very simple.
19:204 bags.
19:214 bags.
19:224 bags.
19:234 bags.
19:244 bags.
19:254 bags.
19:26How many?
19:2715 bags.
19:28So, there will be 15 combination bags.
19:31Which is one option.
19:32Now, what is the total bags?
19:35Total bags.
19:36How many?
19:3725 bags.
19:38How many?
19:394 bags.
19:40So, it will be 25 combination 4.
19:43So, the correct answer will be 15 combination 4 divided by 25 combination 4.
19:49Very, very important.
19:50Very, very important.
19:51So, this is a big question.
19:52A and A probability 1 by 4.
19:53B کی 1 by 2.
19:54Intersection B کی 1 by 8.
19:55Lepin.
19:56A and A union B کی 1 by 8.
19:58A union B کی 1 by 8.
20:00but we are asking A union B's to be a dash
20:03so we have no direct formula
20:06first we have a union B's
20:10which is how we get A's probability plus B's probability minus intersection B's probability
20:16now we have A's half and B's 1 by 4
20:19and we have minus 1 by 8
20:23so L's same to 8
20:258 divided by 4, 8 divided by 2
20:292 plus 4 is 6, minus 1, 5 by 8
20:32so who has 5 by 8?
20:34A union B's
20:36now we have A union B's
20:38when we have a dash in the probability, we have a total probability
20:43we will minus A union B's
20:48now how many A union B's probability?
20:50it's 5 by 8
20:52when you have 5 by 8 minus
20:55then 8 divided by 8
20:568 minus 5
20:57upon 8
20:583 by 8
20:593 by 8
21:00the answer is 3 by 8
21:02so
21:03the question in university is 7 permutation
21:06what will happen?
21:07on the left is 7 vector
21:09on the left is 2 vector
21:10on the left is 7 minus 2 vector
21:13on the left is 7 vector
21:15on the left is 7 vector
21:17on the left is 5 vector
21:18on the left is 5 vector
21:19we will start to open 7 into 6 into
21:22ok
21:23why did we stay at 5 vector
21:24why did we stay at 5 vector
21:26we have to stay at 5 vector
21:27there is also 5 vector
21:285 vector
21:295 vector
21:30will cancel
21:317 to 6
21:32how much will come?
21:33and this is our angle
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