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I have a question regarding combinations and poker! Could someone explain to me why the number of distinct ways to receive a full house from a five card draw is:

13 nCr 1 * 4 nCr 3 * 12 nCr 1 * 4 nCr 2

and not,

13 nCr 2 * 4 nCr 3 * 4 nCr 2

I usually make small mistakes here and there with combinatorics and I can never find a good answer from anyone. Also, I am more interested in the not in this case. Intuitively they seem to say the same thing to me. (choose two distinct denominations, choose 3 cards for the first denomination and 2 cards for the second denomination). Also does anyone have a good way at viewing combinations other than the number of subsets of size r from a set of size n?

Thanks!

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# How to determine combinations correctly

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