Question 423633: Permutations and combinations
you are dealt five cards from an ordinary deck of 52 playing cards. In how many ways can you get a full house? (A full house consists of three of one kind and two of another. For example A-A-A-5-5 and K-K-K-10-10 are full houses.)
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! a full house is three if one type of card and two of another type ___ there are 13 types of cards
there are 4 ways (4C3) to get three of a type , times 13 types , gives 52 ways for three of a kind
there are 6 ways (4C2) to get two of a type , times 13 types , gives 78 ways to get a pair
the one caveat is that you can't have three of a kind AND a pair of the same type
so, 13 types of three of a kind with 12 types of pairs ___ 52 * 72
or, 12 types of three of a kind with 13 types of pairs ___ 48 * 78
the results are the same
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