First slide

Combinations

Question

A set contains (2n + 1) elements. The number of subsets of the set which contain at most n elements

Moderate

A

2ⁿ
B

2ⁿ⁺¹
C

2^2n–1
D

2²ⁿ

Solution

Number of subsets
$\begin{array}{l} =^{2 n + 1} C_{0} +^{2 n + 1} C_{1} + \dots +^{2 n + 1} C_{n} = N (say) \\ ∴ N = 2^{2 n + 1} - N \\ \Rightarrow 2 N = 2^{2 n + 1} \\ \Rightarrow N = 2^{2 n} \end{array}$

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