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: 49


The number of ways to select three city commissioners from a group of six candidates is 20.

Work Step by Step

The order in which the city commissioners are selected does not matter. Thus, this is a problem of selecting 3 people from a group of 6 candidates. We need to find the number of combinations of 6 things taken 3 at a time. Apply the formula, ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ Where $ n=6,r=3$ $\begin{align} & {}_{6}{{C}_{3}}=\frac{6!}{\left( 6-3 \right)!3!} \\ & =\frac{6!}{3!\times 3!} \end{align}$ $=20$
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