Combination of Combinations I am working on solving a problem involving groups of combinations. 
For example,
There are 25 males and 25 females involved in a study. Eight people are expected to be selected for this study. What is the probability of exactly 4 men and 4 women be selected out of the 50 people?
Clearly this is not the same problem. I am hoping to better understand this so that I can apply it as a general rule to similar problems I am trying to explain as a tutor in Algebra to a college student. I taught basic combinations from 2012-2013 but combinations of combinations are well beyond what I was teaching. Any suggestions on how to set up the problem in form?
My current guess to solving this sort of problem is setup in the following form.
$\frac{8!}{\binom{25}{4} * \binom{25}{4}}$

Order doesn't matter here, so the $8!$ is unnecessary. Your idea is close though. We have $\binom{25}{4}$ ways to choose the men, and $\binom{25}{4}$ ways to choose the women. These are independent of each other, so we multiply them. There are $\binom{50}{8}$ ways to choose the participants, so that's the denominator:
$$ \frac{ \binom{25}{4} \binom{25}{4} } { \binom{50}{8}} $$
