Similar to this question, I want to know if the overlap between two samples is significant. However, my items are not unique; I have c distinct colors of items, there are mi items of color i (1 < i < c), and N = ∑mi items total. Does this make a difference?
I have figured out that drawing one sample of n items (without replacement) follows the multivariate hypergeometric distribution. My question is: given two samples of sizes nA and nB, what is the probability that they share exactly k distinct items in common? And really, I'd like my samples to be sets, so I have at most one item of each color in my samples, though this seems to be a harder problem.