# Let $S= \left \{ 1,2,3,\cdots ,100 \right \}.$ The number of non-empty subsets A of S such that the product of elements in A is even is : Option 1)$2^{50}\left ( 2^{50}-1 \right )$      Option 2)$2^{100}-1$Option 3)$2^{50}-1$Option 4)$2^{50}+1$

Number of sub set of a set -

If a set has n elements, then it has 2sub set.

-

Subsets = Total Subsets - Number of subsets which are odd

= $2^{100}-2^{50}$

= $2^{50}(2^{50}-1)$

Option 1)

$2^{50}\left ( 2^{50}-1 \right )$

Option 2)

$2^{100}-1$

Option 3)

$2^{50}-1$

Option 4)

$2^{50}+1$

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