TITLE: Is there a known distribution for multinomial without replacement?
QUESTION [5 upvotes]: I would like to know if there's a known distribution for a multinomial sampling with limited bin size, or equivalently without replacement. The situation would be that I have $N$ bags of candy holding $k_i, i\in 1..N$ candies within them. Assuming I eat candies randomly from these bags with fixed equal probability $p$, discarding empty bags once I've consumed the last candy, is there a well behaved distribution for the number of candies I've eaten from each bag? Failing that, is there a probability for bag $n$ being empty after $x$ trials?

REPLY [3 votes]: Maybe the multivariate hypergeometric distribution fits your example. See 
Wikipedia's article on this distribution.