## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 701: 10

6

#### 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 1st sentence can be chosen in $1$ ways. The 2nd sentence can be chosen in $1$ ways. Once a sentence is chosen, there is one less left to choose from. The 3rd, 4th and 5th sentences are arranged from the three that are left over. 1. The 1st sentence can be chosen in $1$ ways. 2. The 2nd sentence can be chosen in $1$ ways. 3. The 3rd sentence can be chosen in $3$ ways. 4. The 4th sentence can be chosen in $2$ ways. 5. The 5th sentence can be chosen in $1$ ways. Total ways to arrange the sentences: $1\times 1\times 3\times 2\times 1=3!=6$

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