Number and probability of random allocations of n processes to n servers I've been using the Stanford Algorithms (1) Coursera course, and in a description of a problem, the lecturer said that in the problem of allocating n processes to n servers at random, the sample space of allocations is n^n, and each has equal probability.

Intuitively this seems unlikely to me: if you imagine each server having a number and that number being the number of processes assigned, you wouldn't have the case of two servers being assigned n processes; yet the n^n -- as far as I can see -- assumes that such allocations are possible.

Am I missing something?
The number $n^n$ can be easily obtained if you think the problem in the other direction: each process has $n$ choices and therefore $n$ processes has $n^n$ possible choices in total. Of course it is impossible that two servers have $n$ processes. If a process can be assigned to more than one server, the number of possible assignments is far more than $n^n$.