## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 700: 6

24

#### 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 5th perfomance is "reserved" for the singer that requested so. Once a performer is chosen, there is one less left to choose from. So, 1. The 1st singer can be chosen in $4$ ways. 2. The 2nd singer can be chosen in $3$ ways. 3. The 3rd singer can be chosen in $2$ ways. 4. The 4th singer can be chosen in $1$ ways. 5. The 5th singer can be chosen in $1$ ways. Total ways to arrange the performances: $4\times 3\times 2\times 1\times 1=4!=24$

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