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Question

A subset A of the set X=1,2,.....100 is chosen at random. The set X is reconstructed by replacing the elements of A, and another subset B of X is chosen at random. The probability that AB contains exactly 10 elements is

A
100C10(34)90
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B
100C10(11)100
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C
100C103904100
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D
none of these
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Solution

The correct option is B 100C103904100
The number of ways in which 10 elements will be common:
C10010390
{C10010 for selecting the 10 common elements and 390 for the other 90 elements which can be either in A or in B or in neither}.
Hence, probability = C100103904100
{4100 is used since each elements has 4 options: be either in A or in B or in both or in neither}
Hence, (C) is correct.

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