Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 768: 56



Work Step by Step

Use the formula of permutation: $_{n}$P$_{r}$=$\frac{n!}{(n-r)!}$.You have two permutation problems:$_{5}$P$_{3}$ and $_{5}$P$_{2}$.Solve each one seperately and divide the solutions in the end: -->$_{n}$P$_{r}$=$\frac{n!}{(n-r)!}$ $_{5}$P$_{3}$=$\frac{5!}{(5-3)!}$ -simplify- $_{5}$P$_{3}$=$\frac{5!}{2!}$ -write using factorial- $_{5}$P$_{3}$=$\frac{5*4*3*2*1}{2*1}$ -simplify- $_{5}$P$_{3}$=60 -->$_{n}$P$_{r}$=$\frac{n!}{(n-r)!}$ $_{5}$P$_{2}$=$\frac{5!}{(5-2)!}$ -simplify- $_{5}$P$_{2}$=$\frac{5!}{3!}$ -write using factorial- $_{5}$P$_{2}$=$\frac{5*4*3*2*1}{3*2*1}$ -simplify- $_{5}$P$_{2}$=20 Divide the solutions: 60$\div$20=3.So $_{5}$P$_{3}$ $\div$ $_{5}$P$_{2}$=3
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