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In poker, a hand with  cards has two pairs if it contains two cards of one rank, two cards of a different rank, and a fifth card that does not match either of the first two ranks. (For example, the hand JJ774 has two pairs.) The order of the cards does not matter (so JJ774 and 7J74J are the same). How many hands with  cards have two pairs? (All the cards are taken from a standard deck of  cards.)

 Dec 21, 2019
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There are 52 ways of choosing the first card, and 3 ways of choosing its pair.

There are 48 ways of choosing the next number, and 3 ways of choosing its pair.

There are 44 ways of choosing the single card, which gives us 52*3*48*3*44 = 988416 ways.

 Dec 21, 2019

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