Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.1 - The Basics of Counting - Exercises - Page 396: 15



Work Step by Step

Let us consider a string of length n. No. of choices: n No. of options in each choice: 26 Therefore, no. of strings of length n = $26\times26\times ... \times26$ [n times] =$26^n$ So, number of strings of length four or less = $26^1+26^2+26^3+26^4$ =($1+26^1+26^2+26^3+26^4$)-1 =$\frac{26^5-1}{26-1}$-1 =475255-1 =475254 Including the empty string, we have 475255.
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