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How many five-card poker hands using 52 cards contain exactly two aces?

I know the answer is $$\binom{4}{2}\cdot \binom{48}3,$$ but I'm not sure how to explain it.

Any help here?

2 Answers 2

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There are $52$ two cards, $4$ aces and $48$ other non-ace cards. When you are choosing a hand with $2$ aces, there are $C(4,2)$ ways to choose the two aces and $C(48,3)$ ways to choose the other cards.

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    To add to this, the reason these terms are multiplied together to get the final answer is that there are $C(48,3)$ ways to choose the other cards for each of the $C(4,2)$ ways to choose the aces. – 2017-02-03
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    .... sometimes referred to as the [Rule of Product](https://en.wikipedia.org/wiki/Rule_of_product) – 2017-02-03
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    @amWhy cool! I never knew it had a name – 2017-02-03
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You are choosing two of the four aces and three of the remaining $48$ cards. The choices are independent.