5 men and 5 women randomly pair up.

The probability that all pairs consist of a man and a woman each is $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers.

What is $a+b$ ?

The answer is 71.

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One of the men sees 4 men and 5 women,the probability being 5/9 since he can't pair himself.The next man sees 3 men and 4 women in which the probability is 4/7 doing the same for the rest of the men,we get (5/9)(4/7)(3/5)(2/3)(1) and this equals to 8/63 and 8+63 is 71