Hypergeometric probability question After learning some probability, I've found out that exercises and tasks are very simplified for the sake of learning. So I don't really know what is the correct way to solve the following problem:

A bag has 10 white, 10 brown, 10 green, 10 yellow marbles. We take 15
  out of it, what's the probability that the 15 will be 10 white and 5
  yellow?

I know it's a fraction with 40 choose 15 in the denominator, but what about the numerator? We need to multiply 15 choose 10 and 15 choose 5, yes. But do we include 15 choose 0 twice? All the exercises have only two colors of marbles in the bag or two possible groups, so I don't know what to do when there are more groups and one of them isn't in the result.

It's the multivariate hypergeometric distribution with the pdf of a vector $(Y_1,Y_2,\dots,Y_k)$ given by:
$$\Pr(\small{Y_1 = y_1, Y_2 = y_2, \ldots, Y_k = y_k}) = \frac{\binom{m_1}{y_1} \binom{m_2}{y_2} \cdots \binom{m_k}{y_k}}{\binom{m}{n}}, \quad (y_1, y_2, \ldots, y_k) \in \mathbb N^k ;\; \sum_{i=1}^k y_i = n$$
Hence,
$$\Pr(\small{W=10;B=0;G=0;Y=5})=\frac{{10\choose 10} {10\choose 0}{10\choose 0}{10\choose 5}}{40\choose 15}=\frac{{10\choose 5}}{40\choose 15}$$
