First slide

Combinations

Question

A set contains $(2n+1)$ elements. If the number of subsets of this set which contain at most n elements is 4096, then n is

Difficult

A

15
B

13
C

6
D

21

Solution

$^{2 n + 1} c_{0} +^{2 n + 1} c_{1} + - - - - +^{2 n + 1} c_{n} = 4096$
$\Rightarrow \frac{2^{2 n + 1}}{2} = 4096$

$2^{2 n} = 4096 = 2^{12}$

$\Rightarrow n = 6$

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