Problem

A total of 2n people, consisting of n married couples, are randomly divided into n pairs....

A total of 2n people, consisting of n married couples, are randomly divided into n pairs. Arbitrarily number the women, and let Wi denote the event that woman i is paired with her husband.

(a) Find P(Wi).


(b) For i ≠ j, find P(Wi\Wj).


(c) When n is large, approximate the probability that no wife is paired with her husband.


(d) If each pairing must consist of a man and a woman, what does the problem reduce to?

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