SOLUTION: A hand consists of 4 cards from a​ well-shuffled deck of 52 cards.
a. Find the total number of possible 4-card poker hands.
b. A black flush is a 4-card hand consisting of
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-> SOLUTION: A hand consists of 4 cards from a​ well-shuffled deck of 52 cards.
a. Find the total number of possible 4-card poker hands.
b. A black flush is a 4-card hand consisting of
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Question 1039945: A hand consists of 4 cards from a well-shuffled deck of 52 cards.
a. Find the total number of possible 4-card poker hands.
b. A black flush is a 4-card hand consisting of all black cards.Find the number of possible black flushes.
c. Find the probability of being dealt a black flush. Answer by jim_thompson5910(35256) (Show Source):
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Part A)
Let's determine how many ways to pick 4 cards from a pool of 52.
n = 52
r = 4
n C r = (n!)/(r!(n-r)!)
52 C 4 = (52!)/(4!*(52-4)!)
52 C 4 = (52!)/(4!*48!)
52 C 4 = (52*51*50*49*48!)/(4!*48!)
52 C 4 = (52*51*50*49)/(4!) ... the 48! terms cancel.
52 C 4 = (52*51*50*49)/(4*3*2*1)
52 C 4 = (6497400)/(24)
52 C 4 = 270725
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Part B)
There are 26 black cards (spades and clubs).
Let's determine how many ways to pick 4 cards from a pool of 26.
n = 26
r = 4
n C r = (n!)/(r!(n-r)!)
26 C 4 = (26!)/(4!*(26-4)!)
26 C 4 = (26!)/(4!*22!)
26 C 4 = (26*25*24*23*22!)/(4!*22!)
26 C 4 = (26*25*24*23)/(4!) ... the 22! terms cancel.
26 C 4 = (26*25*24*23)/(4*3*2*1)
26 C 4 = (358800)/(24)
26 C 4 = 14950
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Part C)
Divide the results of part B over part A
(result of part B)/(result of part A) = 14950/270725 = 0.05522208883553
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Summary:
Answer to part A: 270725
Answer to part B: 14950
Answer to part C: 0.05522208883553
Answer to part C is approximate. Make sure to round it however the book instructs.
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