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

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Question 1114279: In a deck of 52 playing cards (jokers not allowed), how many five-card poker hands containing three of a kind (but not a full house or four of a kind) are possible?
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
We can choose the suits of the three of a kind in 4C3 ways

We can choose the rank of the three of a kind in 13C1 ways.

That leaves 12 ranks from which to choose the two remaining cards.

We can choose the ranks of the two remaining cards in 12C2 ways.

We can choose the suit of the lower ranking of the two in 4C1 ways.

We can choose the suit of the higher ranking of the two in 4C1 ways.

Answer: 4C3∙13C1∙12C2∙4C1∙4C1 = 4∙13∙66∙4∙4 =  54912

Edwin
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