## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1104: 61

#### Answer

The number of ways in which a group of 3 members is to be selected out of 20 people to attend a conference is $1140$.

#### Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, \begin{align} & n=20 \\ & r=3 \\ \end{align} Then, we have to find the number of combinations of 20 things taken 3 at a time: \begin{align} & {}_{20}{{C}_{3}}=\frac{20!}{3!\left( 20-3 \right)!} \\ & =\frac{20!}{3!17!} \\ & =\frac{20\times 19\times \ldots \times 17!}{3!17!} \\ & =1,140 \end{align} Thus, the number of ways in which a group of 3 members is to be selected out of 20 people to attend a conference is $1140$.

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