SOLUTION: If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different hands consist of the following:
Three of a kind?
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Three of a kind?
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Question 1109615: If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different hands consist of the following:
Three of a kind? Answer by Edwin McCravy(20055) (Show Source):
Choose the common rank of the three in 13C1 ways.
Choose the suits for the three in 4C3 ways
Choose the two different ranks of the other two cards in 12C2 ways,
to prevent the hand from being either four of a kind or a full
house.
Choose the suit for the higher ranking other card in 4C1 ways.
Choose the suit for the lower ranking other card in 4C1 ways.
Answer: (13C1)(4C3)(12C2)(4C1)(4C1) = 54912 ways.
Edwin
