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: 54


The number of ways to select 18 people from 100 for the the required committee is $3.0664511e+19$.

Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, $\begin{align} & n=100 \\ & r=18 \\ \end{align}$ Then, we have to find the number of combinations of 100 things taken 18 at a time: $\begin{align} & {}_{100}{{C}_{18}}=\frac{100!}{18!\left( 100-18 \right)!} \\ & =\frac{100!}{18!82!} \\ & =\frac{\left( \begin{align} & 100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times \\ & 91\times 90\times 89\times 88\times 87\times 86\times 85\times 84\times 83\times 82! \\ \end{align} \right)}{\left( \left( 82! \right)\times 18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right)} \\ & =3.0664511e+19 \end{align}$
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