SOLUTION: Suppose you have a deck of 52 playing cards (no jokers) A. How many five-card hands containing exactly three aces are possible? B. How many five-card hands containing exactly thr

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Question 1126830: Suppose you have a deck of 52 playing cards (no jokers)
A. How many five-card hands containing exactly three aces are possible?
B. How many five-card hands containing exactly three of a kind are possible?
Answer by math_helper(2461) About Me  (Show Source):
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A. C(4,3)*C(48,2) =

B. C(4,3)*C(48,2)*C(13,1) = +highlight%28+58656+%29+
As "three of a kind" is a specific type of poker hand, I should mention this answer includes full-houses (where the non-triplicate cards match in rank).

To exclude full-houses, note that there are C(13,1)*C(4,3)*C(12,1)*C(4,2) = 3744 of them, so you would have 58656-3744 true "three of kind" poker hands.