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Let S = (1, 2, …, 20}. A subset B of S i...

Let S = (1, 2, …, 20}. A subset B of S is said to be ''nice'', if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is ''niche'' is

A

`(6)/(2^(20))`

B

`(4)/(2^(20))`

C

`(7)/(2^(20))`

D

`(5)/(2^(20))`

Text Solution

Verified by Experts

The correct Answer is:
D
Number of subset of `S=2^(20)`
Sum of elements in S is `1+2+......+20=(20(21))/2=210 `
`[therefore 1+2+......+n=(n(n+1))/2]`
Clearly , the sum of elements of a sunset would be 203 , if we consider it as follows
S -{7},S --·{1,G}S-{2,5},S-{3,4}
S-{1,2,4)
`therefore` Number of a favoueables cases =5
Hence , required probility `=5/(2^(20)`
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