SOLUTION: A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of (a) four hearts and one spade? (b) three red card

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Question 520629: A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of (a) four hearts and one spade? (b) three red cards and two black cards? (c) at least 3 face cards? (d) 2 aces and 2 face cards?
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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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Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
a)13C4*13C1=715*13=9295
b)26C3*26C2=2600*325=845000
c)12C3*40C2+12C4*40C1+12C5=171600+19800+792=192192
d)4C2*12C2*36C1=156816
.
Ed