SOLUTION: In a deck of 52 playing cards (jokers not allowed), how many five-card poker hands consisting of three of a kind and a pair (a full house) are possible?

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Question 1174216: In a deck of 52 playing cards (jokers not allowed), how many five-card poker hands consisting of three of a kind and a pair (a full house) are possible?
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Here are a couple of different ways to calculate the number. When working with probability, it is good to be able to see that two different paths lead to the same answer.

First method....

(1) choose 2 of the 13 ranks to be the ones in the hand;
(2) choose 1 of those 2 to be the one of which there are 3;
(3) choose 3 of the 4 of the first rank;
(4) choose 2 of the 4 of the other rank

Second method....

(1) choose one of the 13 ranks to be the one with 3 cards of that rank;
(2) choose 3 of the 4 cards of that rank;
(3) choose one of the other 12 ranks to be the one with 2 cards;
(4) choose 2 of the 4 cards of that rank