In the wikipedia link http://en.wikipedia.org/wiki/Hypergeometric_distribution it is obvious you can do things like "I draw 5 cards from a deck of 50 cards where there are 10 cards that equate to success, 40 that fail, and I want to know the probability of drawing 2 success cards", but in the multivariate version at http://en.wikipedia.org/wiki/Hypergeometric_distribution#Multivariate_hypergeometric_distribution it seems you have to pick the exact amount of things you want to draw, and draw exactly that many. i.e.
I draw 10 cards from a deck with 10 red cards, 15 blue cards, and 5 blank cards, and want to draw exactly 3 blank cards, 6 red cards, and 1 blue card.
How do I use the multivariate distribution method, to allow for wildcards or unsure draws, i.e. I want to draw at least 3 blank cards given the same example above, but don't care about what else I draw?
I tried using the binomial coefficient "X choose Y" given that X is the total number of marbles/cards/whatever in the pile, and Y is the number of wildcards, but it didn't work. It gave me wildly incorrect results.
EDIT: Probability without replacement question The top answer seems good, and it solves one of my problems (for example now I can put a deck of cards that has three types of unique cards in it, 3 of each kind of card, pick one card and figure out the probability of drawing it if I draw 1, 2, 3, etc. cards from the deck) but now I can't pick more than one type of card that I want to draw from the deck. So... Is there a way to use the technique in section "A" in the above question's answer, to do this if I want to grab multiple different types of cards?