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: 63

Answer

The number of ways of forming a four-letter password is $840$.

Work Step by Step

We know that: ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ So, from the information, $\begin{align} & n=7 \\ & r=4 \\ \end{align}$ Then, we have to find the number of permutations of 7 things taken 4 at a time: $\begin{align} & {}_{7}{{P}_{4}}=\frac{7!}{\left( 7-4 \right)!} \\ & =\frac{7!}{3!} \\ & =\frac{7\times 6\times \ldots \times 3!}{3!} \\ & =840 \end{align}$ Thus, the number of ways of forming a four-letter password is $840$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.