## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2: 49

180

#### Work Step by Step

The number of permutations of n items, where p items are identical, q items are identical, r items are identical, and so on, is given by: $\frac{n!}{p!q!r!}$ The number of distinct ways the letters of the word DALLAS can be arranged: $\frac{6!}{2!2!}$ = $\frac{6*5*4*3*2*1}{2*1*2*1}$ = 180 ways

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