- #1

utkarshakash

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## Homework Statement

Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is

## Homework Equations

## The Attempt at a Solution

Total number of subsets possible is 2^n. Now the subsets containing 1 element=n. For 2 elements it is n(n-1). Similarly for n elements it is n!. Now A and B can belong to any one of the above.

[itex]P=\dfrac{^nC_2+^{n(n-1)}C_2+^{n(n-1)(n-2)}C_2.........+^{n!}C_2}{^{2^n}C_2}[/itex]