Question:
Let $S=\{1,2,3, \ldots .100\}$. The number of nonempty subsets A of S such that the product of elements in A is even is :-
Correct Option: , 4
Solution:
$S=\{1,2,3 \cdots-100\}$
$=$ Total non empty subsets-subsets with product of element is odd
$=2^{100}-1-1\left[\left(2^{50}-1\right)\right]$
$=2^{100}-2^{50}$
$=2^{50}\left(2^{50}-1\right)$