Say I have T balls, B of them black and T-B of them white.
I have N bins, each with a maximum capacity of T/N (that is, when the balls are all placed into the bins, all bins have the same number of balls, so assume T is always exactly divisible by N).
The balls are randomly assigned to the bins.
What is the probability that each of the bins has at least one black ball?
I figured out the probability that a given bin has a black ball, but I'm quite stuck at how to proceed - it doesn't seem that knowing the probability for a given bin helps me.