Let S={1,2,...,20} A subset B of S is sa...

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

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

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

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

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

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The correct Answer is:

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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