## Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education

# Chapter 6 - Section 6.1 - The Basics of Counting - Exercises - Page 396: 16

66351

#### Work Step by Step

Let's first find the total number of strings of four lowercase letters There are 26 letters in the alphabet. So, number of choices: 4 no. of options: 26 therefore the number of words = $26\times26\times26\times26=26^4$ Now, let's find the number of strings of four lowercase letters which $do$ $not$ have $x$ in them. As if the alphabet didn't have $x$ in it. So, number of choices: 4 no. of options: 25 (all the letters except $x$) therefore the number of words without any $x$ = $25\times25\times25\times25=25^4$ therefore the number of words with at least one $x$ = the total number of words - the number of words without any $x$ =$26^4 - 25^4$ =456976 - 390625 =66351

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