Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2: 12

Answer

120

Work Step by Step

Of the 7 places on the bench, places 4 and 5 are taken by the counselor and the troublesome camper. So, there are 5 places to be filled by 5 remaining campers. 1. The camper for the 1st place can be chosen in 5 ways. 2. The camper for the 2nd place can be chosen in 4 ways. 3. The camper for the 3rd place can be chosen in 3 ways. 4. The camper for the 4th place can be chosen in 2 ways. 5. The camper for the 5th place can be chosen in 1 ways. The total number of arrangements is $5\times 4\times 3\times 2\times 1=120$
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