## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1104: 48

#### Answer

The number of arrangements that can be made using four of the letters of the word COMBINE is 840.

#### Work Step by Step

We need to choose 4 letters from a group of 7 letters. The order in which the letters are chosen matters because 7 letters of the word "COMBINE" are distinct. Therefore, we need to find the number of permutations of 7 things taken 4 at a time. Apply the formula, ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ Where $n=7,r=4$ \begin{align} & {}_{7}{{P}_{4}}=\frac{7!}{\left( 7-4 \right)!} \\ & =\frac{7!}{3!} \end{align} Solve further: \begin{align} & {}_{7}{{P}_{4}}=\frac{7\times 6\times 5\times 4\times 3!}{3!} \\ & =7\times 6\times 5\times 4 \\ & =840 \end{align}

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