Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 756: 56



Work Step by Step

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