Suppose that n people are each randomly assigned a number from 1 to m with replacement.  What is the probability that exactly one number is assigned to more than one person?  

What I have tried:

Defining the event A to be 'exactly one number is assigned to more than one person', I can see that the probability of A is 0 when m=n and 1 when m<n.
For m>n, the sample space would be m^n. I have written out the sample space for n=3 and m=4. In this case, P(A)=40/64=5/8. However, I cannot see how to compute the number of sample points in the general case.