For how many non-empty subsets of S is the product of the elements

Question

S={1,2,3,.....400}.
For how many non-empty subsets of S is the product of the elements of the subset equal to an even number?
A) 2^400-2^300
B) 2^400-2^100
C) 2^400-2^200
D) 2^200
E) 2^300

niks18 · Answer

For any set having  n  elements, number of subset  = 2^n

Here we have  400  elements, total number of subsets  = 2^{400}

Now we need a subset whose elements' product yield an even number. So from the total subset we need to remove ODD element subset

From  1  to  400  we have  200  elements that are odd. So number of subsets that have  ONLY ODD  elements  = 2^{200}

Hence required No  = 2^{400}-2^{200}

Option  C

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For how many non-empty subsets of S is the product of the elements

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