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A set has (2n + 1) members. If the total number of its subsets having no more than n elements is 4096, then what is the value of n?

1. 6
2. 15
3. 21
4. None of these

Correct answer: 6

Solution

For a set of 2n+1 elements, by symmetry C(2n+1,k)=C(2n+1,2n+1-k), the number of subsets with at most n elements is exactly half of 2^(2n+1), i.e. 2^(2n) = 4^n. Setting 4^n = 4096 = 4^6 gives n = 6.

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