Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1104: 60


The number of ways to award the prize to three people out of 50 people (if the first prize is $\$1000$, second prize is $\$500$, and third prize is $\$100$) is $117,600$.

Work Step by Step

We know that the number of ways in which r number of things are arranged from n number of things is obtained by: ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ So, from the information, $\begin{align} & n=50 \\ & r=3 \\ \end{align}$ Then, we have to find the number of permutations of 50 things taken 3 at a time: $\begin{align} & {}_{50}{{P}_{3}}=\frac{50!}{\left( 50-3 \right)!} \\ & =\frac{50!}{47!} \\ & =\frac{50\times 49\times 48\times 47!}{47!} \\ & =117600 \end{align}$ Thus, the number of ways is $117,600$.
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