Suppose a deck of 20 cards contains four red cards four whit

Suppose a deck of 20 cards contains four red cards, four white cards, four blue cards, four green cards, and four black cards. If 10 cards are selected at random from this deck, without replacement, what is the probability that each possible color will occur exactly twice?

There are 20C10 ways to choose any 10 cards.

Meanwhile, there are 4C2 ways to choose two of each color, so there are (4C2)^5 ways to do the said job.