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: 66


The number of possible bowls of different flavors of ice cream is $4,495$

Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, $\begin{align} & n=31 \\ & r=3 \end{align}$ Then, we have to find the number of permutations of 31 things taken 3 at a time: $\begin{align} & {}_{31}{{C}_{3}}=\frac{31!}{3!\left( 31-3 \right)!} \\ & =\frac{31!}{3!28!} \\ & =\frac{31\times 30\times 29\times 28!}{6\times 28!} \\ & =4,495 \end{align}$
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