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Let n be an odd number and X be a set with n elements. Find the...

Let n be an odd number and X be a set with n elements. Find the no. of subsets of X which has even no. of elements. The answer should be a number depending only on n. (For example, when n = 5, you need to find the no.of subsets of X which has either 0 elements or 2 elements or 4 elements)

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Answer #1

Number of subsets of X which has 0 elements is 1 (empty set only), number of subsets of X which has 2 elements is C(n,2),... and number of subsets of X which has n-1 elements is C(n,n-1). So number of subsets of X which has even number of elements is 1+C(n,2)+C(n,4)+...+C(n,n-1).

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