Hi everyone, here is my question:

Suppose there are "b" balls and n bins, we like to put all balls into "n" bins and the probability that every ball falls into any bin is same(1/n).

Is there a simple equation/series of equations to calculate the probability that there are x bins (0<x<=n) with at least one ball in it?

I know this can be done by counting or permuting all possible outcomes but this is not feasible when b and n are large.

Please advise.