5 men and 5 women

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

The number of ways in which ten people can be paired up is $\frac{10!}{2^5\cdot 5!} = 945$

The number of ways in which they can pair up with a man and woman in each pair is: $5! = 120$

So the probability is: $P = \frac{120}{945} = \frac{8}{63}$

$8+63 = \boxed{71}$