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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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13 Oct 2017, 21:05
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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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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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For how many non-empty subsets of S is the product of the elements   [#permalink] 14 Oct 2017, 00:37
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# For how many non-empty subsets of S is the product of the elements

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