- #1

mr_coffee

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Supose that you are dealt four cards instead of 5. How many 4 card hands consist of two pairs (two cards of one denomination and two cards of a second denomoniation)?

The answer is 2,808.

It was found by:

(13 choose 2) * (4 choose 2)^2

But I'm confused because if you are choosing 2 cards of one denomination, that's like choosing two 5's. There is only one 5 in every 13 cards or suites correct?

so if you have

(13 choose 2) that means your choosing 2 cards out of 1 suit weither it be hearts, diamonds, clubs or spades. So how can you be choosing 2 of the same numbers from a set of 13?

Or are they saying, they are chooosing 2 cards of 1 suit, such as a 4 and a 10, and later they are choosing 2 cards to match that suit, such as a 10H and a 10C, that would be one (4 choose 2) and the other would be 4H, and a 4D that would be the other (4 choose 2)?

I think i got it by writing this question but just making sure, thanks!