Question

# Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

A
2101220
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B
20C10210
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C
2101210
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D
20C10220
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Solution

## The correct option is D 20C10220Total number of subsubsets of set X=210=1024 Number of subsets with zero element =10C0 Number of subsets with one element =10C1 Number of subsets with two elements =10C2 . . . . Number of subsets with 10 elements =10C10 A & B are taken from P(X) from 210 subsets so total ways =210×210 Number of ways such that A and B have equal number of elements=(10C0)2+(10C1)2+(10C2)2+........+(10C10)2 =20C10 Required probability =20C10220

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