Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Section 12.2 Permutations and Combinations - 12.2 Assess Your Understanding: 35

Answer

$24$ different ways

Work Step by Step

Lining people up involves permutation (because order matters) of 4 distinct objects taken 4 at a time. Use the formula $P(n,r)=\dfrac{n!}{(n-r)!}$: $P(4,4) \\= \dfrac{4!}{(4-4)!} \\= \frac{4\times3\times2\times1}{0!} \\= \dfrac{24}{1} \\= 24$ Thus, 4 people can line up in 24 different ways.
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