Question 520629
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. 
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How many different hands are there consisting of 
(a) four hearts and one spade?
# of ways to get 4 hearts: 13C4 = 715
# of ways to get 1 spade: 13C1 = 13
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Total # of ways = 715*13 = 9295
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(b) three red cards and two black cards? 
# of ways to get 3 red = 26C3 = 2600 
# of ways to get 2 black = 26C2 = 325
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Total # of ways = 845,000
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(c) at least 3 face cards?
There are 12 face cards:
3 face cards: 12C3*40C2 = 220*780 
+ 4 face cards:  12C4*40C1 = 495*40 
+ 5 face cards: 12C5*40C0 = 792*1
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Total # =  171600 + 19800 + 792 = 192,192
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(d) 2 aces and 2 face cards?
# of ways to get 2 aces: 4C2 = 6
# of ways to get 2 face cards: 12C2 = 66
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Total # of ways = 6*66 = 396
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Cheers,
Stan H.
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