SOLUTION: 2 questions that my daughter and I have been trying to answer: 1) find the number of possible 5-card hands that contain the cards specified: 3 of one kind (kings, queens and so on)

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Question 447757: 2 questions that my daughter and I have been trying to answer: 1) find the number of possible 5-card hands that contain the cards specified: 3 of one kind (kings, queens and so on) and 2 of a different kind.
2) find the number of possible 3-card hands that contain: 3 of one kind (kings queens and so on)
Thank you so much!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1) find the number of possible 5-card hands that contain the cards specified:
3 of one kind (kings, queens and so on) and 2 of a different kind.
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Pick a card type: 13 ways
Pick 3 of those cards: 4C3 = 4 ways
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Pick another card type: 12 ways
Pick 2 of those cards: 4C2 = 6 ways
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Total number of 3 of a kind and 2 of a kind = 13*12*4*6 = 3744 hands
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2) find the number of possible 3-card hands that contain: 3 of one kind (kings queens and so on)
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Pick a card: 13 ways
Pick 3 of that card: 4C3 = 4 ways
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Total # = 13*4 = 52 3-of-a-kind hands
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Cheers,
Stan H.