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Question

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 ''nice'' is :

A
5220
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B
6220
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C
4220
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D
7220
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Solution

The correct option is A 5220
S={1,2,,20}
Total number of subsets of S is 220.
Sum of elements of S is 20×212=210.
Sum of the elements of B is 203

So, we have to remove elements x1,x2,...,xn from S such that x1+x2+...+xn=7

The possible sets are
i.e. {7},{1,6},{2,5},{3,4},{1,2,4}
Required probability =5220

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