A set S contains (2n+1) elements. There are 4096 subsets of S which contain at <strong>MOST</strong> n elements. What is n equal to?
- A. 5
- B. 6 ✓
- C. 7
- D. 8
Correct Answer: B. 6
Explanation
The total number of subsets is 2^{2n+1}. By symmetry of binomial coefficients, the number of subsets with at most n elements is exactly half the total subsets, so 2^{2n+1-1} = 2^{2n}. Given 2^{2n} = 4096 = 2^{12}, we get 2n = 12, hence n = 6.
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