SOLUTION: HI can you explain how you get 3744 ways to get a full house in a standard deck? The question was how many ways can you get a full house?

Question 420771: HI can you explain how you get 3744 ways to get a full house in a standard deck? The question was how many ways can you get a full house?
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 , your 3744 number

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