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: 57


The number of ways in which the first four finishers come in out of 6 competitors is $360$.

Work Step by Step

We know that from the information, $\begin{align} & n=10 \\ & r=4 \\ \end{align}$ Then, we have to find the number of permutations of 6 things taken 4 at a time by applying the above formula: $\begin{align} & {}_{6}{{P}_{4}}=\frac{6!}{\left( 6-4 \right)!} \\ & =\frac{6!}{2!} \\ & =\frac{6\times 5\times 4\times 3\times 2!}{2!} \\ & =360 \end{align}$ Thus, there are $360$ ways.
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