Chapter 8.5, Problem 41E

To determine

To find: the number of ways the officers can be filled.

Answer to Problem 41E

The number of ways the officers can be filled 11880.

Explanation of Solution

Given information:

From a pool of 12 candidates, the officers of president, vice president, secretary, and treasure will be filled.

Calculation:

The number of permutations of $n$ elements taken $r$ at a time is

  $\begin{array}{c}{}_n{P}_r=\frac{n!}{\left(n-r\right)!}\\ =n\left(n-1\right)\left(n-2\right)\mathrm{...}\left(n-r+1\right)\end{array}$

We need to arrange four out of the 12 candidates to fill the positions in all the possible ways, since the order of choosing the candidates maters in this job assignment we need to permute them and not take a combination of them.

  $\begin{array}{c}{}_{12}{P}_4=\frac{12!}{8!}\\ =12\times 11\times 10\times 9\\ =11880\end{array}$