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: 59


The number of ways to select 6 people out of 13 people to test the effectiveness of the experiment is $1,716$.

Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, $\begin{align} & n=13 \\ & r=6 \end{align}$ Then, we have to find the number of combinations of 13 things taken 6 at a time: $\begin{align} & {}_{13}{{C}_{6}}=\frac{13!}{6!\left( 13-6 \right)!} \\ & =\frac{13!}{6!7!} \\ & =\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!} \\ & =1,716 \end{align}$
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