Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.6 - Counting Principles - 11.6 Exercises - Page 825: 72


35 diagonals.

Work Step by Step

We must select two vertices among ten vertices. The order in which they are selected is not important. So, we have $_{10}C_2$ different combinations: $_{10}C_2=\frac{10!}{(10-2)!~2!}=\frac{10\times9\times8!}{8!~2!}=45$ But, among those 45 combinations, 10 are sides. $Diagonals=45-10=35$
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