What type of statistical distribution applies to this example

I need to know the type of distribution so that I can calculate the probability function. Here's the example:

Suppose you have some marbles that come in six different colors. You put exactly three marbles of each color into a hat so that the hat contains a total of 18 marbles.

Now suppose you randomly draw 8 marbles from the hat (without looking). What is the probability that you will have drawn exactly 4 of the 6 colors? What's the probability that you would draw all six colors in, say, 10 draws? Another, related question is, How many marbles must you draw before the probability of drawing all six colors reaches 90%?

If anyone knows what statistical distribution this example illustrates, I can look up the probability functions and calculate p(x).

Extra info: The Hypergeometric distribution comes close, but I think it's different in that there are only two colors of marbles in the hat.

Thank you!

OK Ted---based on what I read about the H-dist I think an extension called the Multivariate H distribution is what you're looking for. Check it out at wikipedia.

This is the multinomial distribution - see http://en.wikipedia.org/wiki/Multinomial…
You might be able to guess the form since it a natural extension of the hypergeometric distribution.

Good luck

hey you:
http://vn.answers.yahoo.com/question/ind…