Question

how many 5-card hands that can be dealt off of a 52-card deck, such that two cards are clubs and 3 are hearts?

Answer 1

• 22308

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There are 13 clubs and 13 hearts in the deck.

First, find the number of ways to choose 2 clubs out of 13:

• C(13, 2) = 13! / (2!(13-2)!) = 78 combinations

Next, find the number of ways to choose 3 hearts out of 13:

• C(13, 3) = 13! / (3!(13-3)!) = 286 combinations

Now, multiply these two results:

• 78 * 286 = 22308 possible hands