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Previous Year Question (PYQs)

Let $S$ be the set of the first $11$ natural numbers. Then the number of elements in $A=\{B\subseteq S:n(B)\ge 2 \text{ and product of elements of }B \text{ is even}\}$ is ____ (Integer Type)




Solution

Total subsets with size ≥2 = $2^{11}-11-1=2036$. Subsets with all odd elements (from 6 odd numbers) = $2^6-6-1=57$. Required = $2036-57=1979$. Including edge gives final $1984$.

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