Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1104: 62

Answer

The number of ways to award the prize to three people out of 50 is $19,600$.

Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, \begin{align} & n=50 \\ & r=3 \\ \end{align} Then, we have to find the number of combinations of 50 things taken 3 at a time: \begin{align} & {}_{50}{{C}_{3}}=\frac{50!}{3!\left( 50-3 \right)!} \\ & =\frac{50!}{3!47!} \\ & =\frac{50\times 49\times \ldots \times 47!}{3!47!} \\ & =19,600 \end{align} Thus, the number of ways to award the prize to three people out of 50 is $19,600$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.