Solved: In 5-card poker, played with a standard 52-card

Chapter 11, Problem 10

(choose chapter or problem)

In 5 -card poker, played with a standard 52-card deck, \({ }_{52} C_{5}\), or 2,598,960, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 2,598,960. Shown in Exercises 7-10 are various types of poker hands and their probabilities. In each exercise, find the probability of not being dealt this type of hand.

                                                                                    Number of Ways the

Type of Hand                    Illustration                           Hand Can Occur                      Probability

Flush: 5 cards                                                                      5108                \(\frac{5108}{2,598,960}\)

of the same suit

(excluding royal

flush and straight

 flush)

Text Transcription:

52_C_5

frac 5108 2,598,960