Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 9 - Counting and Probability - Exercise Set 9.3 - Page 549: 4

Answer

There are a total of 259 arrangement of at most 3 letters form the word NETWORK.

Work Step by Step

Number of arrangements of 1 letter = $C(7,1)$ =7 Number of arrangements of 2 letters = $C(7,1) \times C(6,1)$ = 7$\times$6 = 42 Number of arrangements of 3 letters= $C(7,1) \times C(6,1) \times C(5,1)$ = 7$\times$6$\times$5 = 210 Total = 7+42+210= 259
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