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 - Page 701: 45

Answer

120 ways

Work Step by Step

A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference. The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. ---------------- Order (in which the chosen cars finish) is important, so we count permutations of r=3 cars taken from n=6. The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies. ${}_{6}P_{3}=\displaystyle \frac{6!}{3!}=6\times 5\times 4$ $=$120 ways
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.