## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Review Exercises - Page 1126: 78

#### Answer

The total number of ways in which the offices can be filled is 32,760 ways.

#### Work Step by Step

We know that the order in which the four officers are selected makes a difference as the designation for all the four officers would be different. The ordered arrangement in which the order of the arrangement makes a difference is solved using the concept of permutations. Four officers are to be selected from a club of fifteen members. So, $n=15,r=4$. Thus, \begin{align} & _{15}{{P}_{4}}=\frac{15!}{\left( 15-4 \right)!} \\ & =\frac{15!}{11!} \\ & =\frac{15\times 14\times 13\times 12\times 11!}{11!} \\ & =32,760 \end{align}

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