Question 89947: how many five-poker hands consisting of the following distribution are there?
a- aflush ( all five cards of a signle suit)
b- theree of kind (three aces and two other cards)
c- two pairs ( two aces, two kings and one other card)
d- A straight ( all five cards in a sequence)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! how many five-poker hands consisting of the following distribution are there?
a- aflush ( all five cards of a signle suit)
# of ways to pick a suit = 4
# of ways to get 5 of the 13 cards 13C5
Total # of flush hands = 4*13C5
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b- three of kind (three aces and two other cards)
# of ways to pick three aces = 4C3 = 4
# of ways to pick two other cards = 48C2
# of ways full house hands = 4*48C2
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c- two pairs ( two aces, two kings and one other card)
# of ways to pick two aces = 4C2 = 6
# of ways to pick two kings = 4C2 = 6
# of ways to pick one other card = 44C1 = 44
Total # of ways to get 2 aces, 2 kings, one other = 6^2*44
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d- A straight ( all five cards in a sequence)
# of ways to get a straight pattern of 5 cards = 9
# of ways to pick the 5 cards 4^5
# of straight hands = 9*4^5
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Cheers,
Stan H.
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