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Question from Becky, a student:

How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?

Hi Becky,

Let's try this instead.

How many 5-card poker hands consisting of one jack, one ace and three queens are possible with an ordinary 52-card deck?

There are 4 jacks in the deck so there are 4 choices for a jack.
There are 4 aces in the deck so there are 4 choices for an ace.
There are 4 queens in the deck so there are (4 choose 3) = 6 ways to choose 3 queens.

Hence there are 4× 4 × 6 = 96 5-card poker hands consisting of one jack, one ace and three queens.

Now try your problem,
Penny

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