Math problem help

Looking for some general help on a math/probability problem. At one point I probably knew how to figure this out. Perhaps I should still know, but I can't seem to get it. I'm looking for a general way to figure out the following type of problem...

Given an infinitely (sufficiently) large population of marbles of which 10% are green and 90% are blue, what is the probability of picking 10 marbles of which exactly 3 are green?

I know the chance of picking one green marble is 0.1, and I know that the chance of picking 3 green marbles in a row is 0.001 (0.1 x 0.1 x 0.1). But I'm confused when it comes to figuring in that order is unimportant and that a finite number of marbles is being picked - clearly the chance of picking exactly 3 green marbles in 10 tries is different from picking exactly 3 green marbles in 100 tries. Any help? In the end I'd like to generalize the process - given a population of which X% are a given kind, what is the chance of subsampling exactly Y individuals in Z tries.

Thanks in advance...