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You are dealt 5 cards from a standard deck of 52 cards. How many ways can you be dealt the 5 cards so that they contain two cards of one rank, two cards of another rank, and a fifth card of a third rank? We say that such a hand has two pairs. For example, the hand WW228 has two pairs. (Assume that the order of the cards does not matter.)

 May 14, 2020
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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.

 May 16, 2020

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