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

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For how many non-empty subsets of S is the product of the elements [#permalink]

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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

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For how many non-empty subsets of S is the product of the elements [#permalink]

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New post 14 Oct 2017, 00:37
souvonik2k wrote:
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


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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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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For how many non-empty subsets of S is the product of the elements   [#permalink] 14 Oct 2017, 00:37
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