Permutation probability

Should be easy, but I forget the formula. How do I calculate the probability of a certain number of matches in a permutation?

Lets say I have 10 wives and 10 husbands. The wives are randomly lined up in a row. Then the husbands are lined up randomly lined up in a row. In how many cases will the number of husband-wife matches be 0, 1 , 2 ... 10?

The permutations for an array of n elements is n!. So for two arrays you get n!*n! cases. The propability you ask is p = 1/(n!*n!) and that is if you care for the order of the pairs. If you don,t you have just n! cases. So p = 1/n!.