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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
6220
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B
5220
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C
4220
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D
7220
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Solution

The correct option is C 5220
total no. of ways subset of S can be formed = 220
no. of ways in which word nice comes if sum of the elements = 203

sum of all elements of S = 21×202=210

so sets can be

{1,2,.....5,6,8.....20} in this sum 7 is ommited and this formation of

sum can be done in 5 ways (7,(1,6),(2,5),(3,4),(1,2,4)) ways

probability=5220

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