#### 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,
$\begin{align}
& _{15}{{P}_{4}}=\frac{15!}{\left( 15-4 \right)!} \\
& =\frac{15!}{11!} \\
& =\frac{15\times 14\times 13\times 12\times 11!}{11!} \\
& =32,760
\end{align}$