# How many poker hands contain exactly one ace?

I'm getting tripped up because of the "exactly" part. Can anyone explain how to approach this problem and ones that may be similar. For example, if I wanted a hand that contained exactly three K's, or one K and three 9's.

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One thing that may be helpful if you are stuck is to solve a simpler problem where you can enumerate things to make sure that you have your reasoning right. For example, you could ask yourself how many 3-card poker hands with 1 ace can you make from a deck of cards that has 2 aces and 5 non-aces. Varying the small numbers can also help you find patterns that might allow you to guess the form of the answer. – Michael Joyce Nov 14 '12 at 3:41

There are four ways to pick an ace. The remaining four cards cannot be an ace, and so there are $\binom{48}{4}$ ways to choose them.
Answer. $4\binom{48}{4}$.