00:00Here I have 2N plus 1 elements in a set stored in Kyotshin and we're asked
00:05How many subsets does it have that contain 8 more than N elements? Now many people will get confused.
00:11That he can calculate this formula by counting N elements alone.
00:24That gives us 2N plus 1 C N plus 2N plus 1 C N minus 1 now to 2N
00:34Plus 1 C value up to 0 has been asked, which I will give 1024 is equal to 1024 and
00:43We are asked what is the value of N, which has an identity in any element.
00:49Respect �
00:50In a set S is equal to a set having N elements, then the total number of elements in it
00:56A subset of 2 to the power of N is any set of two elements having two elements A, B.
01:02So there will be this many total sets of 2 to the power element i.e. 4 A, B, A, B and NULL.
01:10Set to Fibad
01:19And the total number of subsets will be 2 to the power N, so how can we write it as 2 to the power N
01:25is equal to 2N plus 1 C0 plus 2N plus 1 C1 plus up to 2N plus 1 C2N plus
01:432N plus 1 C2N plus 1 C2N plus 1
01:48Now we will add another identity here, what is this, NCN is equal to NC0, now how is this
02:02The formula is basically NCR is equal to NCN minus R
02:09In this formula, put the value of R as N,NCN,NC,N minus N i.e. NC0, then this comes
02:17That means here, what is 2N plus 1 C0 equal to?
02:242N plus 1 C2N plus 1 so this one is equal to
02:31This will reduce it by one, that is, 2N plus 1 NCR is equal to NCN minus R
02:41That means we will reduce the value of R by one, that is, we will put 2N, this is equal to this
03:01So this gives us a symbol that this third one here is equal to level to third.
03:08It will happen
03:08Then how long will this Bar Nu Fourth continue like this?
03:14What value do you put for 2N plus 1 CR? Where are we given the value up to N?
03:20So then we'll put N in. 2N plus C N is equal to 2N plus C N minus R
03:29That means 2N plus 1 minus N, that is, this will become
03:35What comes directly after N plus 1? This will go in the middle.
03:42As it goes, it will come in the middle 2N plus 1 C N plus it will come in the upper direct 2N plus 1 C N
03:52plus 1
03:53Because this lower one is growing, what does that tell us? A symmetry is forming throughout.
03:58Went
03:58This right side is equal to the left side, so what can we write?
04:072 into 2N plus 1 C 0 plus up to 2N plus 1 C N symmetry whatever the time
04:18Because it is equal to the right side level, by symmetry, we can derive it from this and write it?
04:24So now you have given its sum, in this equation you have given it up to the n element.
04:30That is, 2N plus 1 C 0 plus 2N plus 1 C 1 plus In this way we get the sum
04:38It is given because 1024 means it is equal to 1024, till here we know
04:47So if we put its value, let it be 1024, that is, 2 into 1024 is equal to the power of 2.
04:58from here
04:59But remember, for a sum of n elements, this is 2 to the power of n elements.
05:052n plus 1 element is
05:08So this formula is 2n plus element, this will become 2 to the power 2n plus 1, so here also put
05:15Let's find 2 to the power of 2n plus 1.
05:17Now find out how much 2 into 1024 becomes 2 into 2 into 2 to the 4 to
05:27the 8 16 32 64 128
05:38256 512 1024 1 2 3 4 5 6 7 8 9 10 Here 2 to the power of 10 is
05:47equal to 2 to the power 2n plus 1
05:49Here 2 to the power 11 is equal to 2 to the power 2n plus 1
05:54simply put GA 2n plus 1 is equal to 11 2n is equal to 10 n is equal to
06:015
06:01So the answer to our question is n is equal to 5
06:05Bye Bye Rai Bye Bye Bye, let me also stare
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