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: 43

Answer

$8,648,640$ arrangements

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 of selecting songs (arrangements) is important, so we deal with permutations of r=7 songs to be taken from n=13. The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies. ${}_{13}P_{7}=\displaystyle \frac{13!}{6!}=13\times 12\times 11\times 10\times 9\times 8\times 7$ $=8,648,640$ arrangements
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