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> **Possible Duplicate:**  
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> [What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?](https://stats.stackexchange.com/questions/24211/what-is-the-probability-of-n-people-from-a-list-of-m-people-being-in-a-random-se) 
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Let's say we have 5 kinds of marbles, 1000 of each, mixed up in a giant tub. I want to know how many I have to draw out (without replacement) before I can be 50/70/90% sure I have at least 1 of each type of marble.

I can write a script to compute every possibility in M draws for M=5 to 4001, and get the probability from that, **but** *(my point is)* I figure there must be a statistical distribution that handles this more directly. Is there a name for such a distribution?

Also, if the counts are not equal (i.e. 100 of type 1, 300 of type 2, ...), is there a distribution that handles that?