In this question, I asked about a confusion I had counting the size of the sample space for allocation of n processes to n servers. Bangye gave a simple answer by approaching the counting problem from the perspective of the choice when allocating each process.
I'd like to know -- to expand my understanding of counting -- how we might count in a different way, from the server perspective: assigning each server to some number of processes.
The obvious problem I see is if I have already allocated one process to a server, I then can't allocate it to another, and so the analysis becomes complicated -- each server-based count is dependent on all other server-based counts.
Is this a common problem, and there's actually a heuristic to know which way to count things?