As much as I like Math, Probabillity has always been one of the subjects that I struggle to develop an intuitive sense for. It's really something I should sit down and relearn one of these days... Anyways, I have a puzzle to present to anyone who would like to try to solve it. Its solution, or any ideas that could help me reach the solution, would be incredibly helpful for developing an Extra Credit Artificial Intelligence that can play a particular Card Game. Here is the problem: 1) You have a standard card deck with 52 cards, 4 suits, cards 2 through Ace per suit, standard stuff. 2) You are dealt a hand of size N, that contains A 4 of a Kinds, B 3 of a Kinds, C 2 of a Kinds, and D singles. So 4*A + 3*B + 2*C + D = N. 3) Given the hand size N, what is the probability of drawing a particular combination of A, B, C, and D? Assume that your input is always correct (so 4*A + 3*B + 2*C + D = N). That might be phrased awkwardly, so feel free to ask questions if that doesn't make any sense. I couldn't find any easy to use resources to solve it on my own in about 20 minutes of research, and really, anything, even a pointer in the right direction, will help tremendously. Thanks!