SOLUTION: Find the number of possible 5-card hands that contain the cards specified: 4 aces and 1 other card. I was able to find the formula for a 5-card hand with 2 aces but I'm lost. Fo

Question 128817This question is from textbook
: Find the number of possible 5-card hands that contain the cards specified: 4 aces and 1 other card. I was able to find the formula for a 5-card hand with 2 aces but I'm lost. For 2 aces, it's C(52,5) - C(48,5) - C(4,1) X C(48,4) but I don't understand all the parts. I know C(52,5) is the total possiblilities of a 5-card hand out of 52 cards and C(48,5) is the 48 remaining cards but I'm not sure about the C(4,1) and the next C(48,4)?
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Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the number of possible 5-card hands that contain the cards specified: 4 aces and 1 other card.
Pick 4 aces in 4C4 = 1 way
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Pick 1 other card in 48C1 = 48 ways
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Total # of hands = 1*48 = 48
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I was able to find the formula for a 5-card hand with 2 aces
Pick 2 aces in 4C2 = 6 ways
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Pick 3 other cards from 50 in 50C3 = 19600 ways
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Total # of hands = 6*19600 = 117600 ways
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Cheers,
Stan H.

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