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Let S={1,2,3,....., 100}. The number of ...

Let `S={1,2,3,....., 100}`. The number of non-empty subsets `A` of `S` such that the product of elements in `A` is even is

A

`2^(50)+1`

B

`2^(50)-1`

C

`2^(100)-1`

D

`2^(50)(2^(50)-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Product is even when atleast one even number is selected therefore number of ways of selecting atleast one even number is `(2^(50)-1)` and number of ways of selecting odd number `=2^(50)`.
`rArr ` Total ways `=2^(50)(2^50-1)`.
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