Number Of Different Poker Hands Average ratng: 4,0/5 2509 reviews
Number Of Different Poker Hands
Algebra -> Probability-and-statistics-> 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 Log On
An Introduction to Thermal Physics Daniel V. Schroeder Problem 2-4 Calculate the number of different 5-card poker hands selected from a standard deck of 52 c. In this video we will go over the number of ways of getting the most common poker or sought poker hands using combinations and the multiplication principle. Choose the 4 ranks (denominations), which 1 of these ranks appears twice, which 2 suits appear for that rank, and which 1 suit appears for each of the other 3 ranks: (13 4)(4 1)(4 2)(4 1)3 = 1, 098, 240 Also known as one pair. Poker hands from highest to lowest 1. Royal flush A, K, Q, J, 10, all the same suit. Two different pairs. Pair Two cards of the same rank.
Number Of Different Poker Hands Against
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): You can put this solution on YOUR website!
For parts A) and B), I will be using the combination formula since order does not matter.
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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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Number Of Different Poker Hands Held
