A five-card poker hand is dealt at random from a standard 52-card deck. Note the

Question

A five-card poker hand is dealt at random from a standard 52-card deck. Note the total number of possible hands is C(52,5)=2,598,960. Find the probabilities of the following scenarios: 1) What is the probability that the hand is any straight flush? (We are including royal flush, so we want all five cards of the same suit, and with consecutive rank like 2,3,4,5,6.) = ?

Explanation / Answer

a) 4C1*48C4 = 778,320 = a b) flush: 13C5*4 = 5,148 this includes straight flushes and royal flushes straight flush: from A-5 to 9-K -> 9 total four suits = 9*4 = 36 royal flush: from 10-A -> 1 total four suits = 1*4 = 4 flush -> 5,148 - 36 - 4 = 5,108 = b c) from b), straight flush -> 36 = c

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