A set contains (2n + 1) elements. number of sub-sets of set which contains at most n elem

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6.Permutation and Combination

normal

A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-

A

$2^{n-1}$

B

$2^{n+1}$

C

$2^{2n}$

D

$2^n$

Solution

$(r=0)$ or $(r=1)$ or $\left( {r = 2} \right) – \, – \, – \,$or $(r=n)$

$^{2 n+1} C_{0}+^{2 n+1} C_{1}+^{2 n+1} C_{2}+\ldots . .^{2 n+1} C_{n}$

$=2^{2 n+1-1}$

$=2^{2 n}$

Standard 11

Mathematics

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