Question 49

Let S = {1,2,...,100}. The number of nonempty subsets T of S such that the, product of numbers in T is even is

Solution

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The number of ways to select non-empty set out of S = 100C1+100C2+100C3+..........100C100 = $$2^{100}$$-1

Similarly, the number of ways to select non-empty set from (say) P= {1,3,5,7,9,...................99} = $$2^{50}$$-1

Hence, the required number of set = $$2^{100}$$-1 - ($$2^{50}$$-1) = $$2^{50}\left(2^{50}-1\right)$$

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