5 card poker hand is dealt from a well-shuffled standard deck of 52 cards. Find the probability of being dealt a flush. (Flush: any five cards of the same suit, excluding straight and royal flushes). straight: 5 cards of sequential rank in the same suit royal flush: a straight of the top 5 cards of the same suit, A 10 J Q K

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
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Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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A 5 card poker hand is dealt from a well-shuffled standard deck of 52 cards. Find the probability of being dealt a flush. (Flush: any five cards of the same suit, excluding straight and royal flushes).

straight: 5 cards of sequential rank in the same suit

royal flush: a straight of the top 5 cards of the same suit, A 10 J Q K

Expert Solution
Step 1

5 card poker game :

Well shuffled deck of 52 cards.

Total ways to select and arrange 5 cards from 52 cards.

NCr :

( 52 C 5) = (52*51*50*49*48)/20

= 2598960

Probability of being dealt with flush =?

Probability =

(favorable outcomes /total outcomes) 

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