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: 5

Answer

120

Work Step by Step

The Fundamental Counting Principle$:$ The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. ----------- The 6th act is "reserved" for the performer that requested so. Once an act is chosen, there is one less left to choose from. So, 1. The 1st act can be chosen in $5$ ways. 2. The 2nd act can be chosen in $4$ ways. 3. The 3rd act can be chosen in $3$ ways. 4. The 4th act can be chosen in $2$ ways. 5. The 5th act can be chosen in $1$ ways. 6. The 6th act can be chosen in $1$ way. Total ways to arrange the acts: $5\times 4\times 3\times 2\times 1\times 1=5!=120$
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