Another balls into bins question...
I have n balls to distribute into k bins which can hold no more than l balls. What probability density function describes the number of balls in a (randomly selected) bin?
i.e. If I pick one of these bins, what is the probability of it containing 0, 1, 2 balls, etc?
To try and clarify a bit, there's not meant to be anything fancy going on here - for each of n balls, pick a non-full bin at random (all non-full bins have equal probability). (Assume n <= kl otherwise the whole thing is fairly meaningless!)