Question 1113745: A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type.
Three of a kind (three of one denomination, one of another denomination, and one of a third)
For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playing cards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), and king (K), and in one of four suits: hearts (), diamonds (), clubs (), and spades (). Thus, for instance, the jack of spades, J, refers to the denomination of jack in the suit of spades.
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Choices for the rank (value) of the triple: 13C1
Choices for the suits of the triple: 4C3 (3 out of 4 suits must be dealt)
Choices for nonmatching 2 cards: 12C2
Choices for suits of the nonmatching 2 cards: (4C1)^2
Total number of three-of-a-kind hands (not categorized as other hands, such as full-house):
(13C1)(4C3)(12C2)(4C1)^2 = 13*4*66*16 = 54912
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Ans: Total number of possible three-of-a-kind hands is 54912
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