Answer
A president, vice president, secretary, and treasurer can be chosen in 5040 ways.
Work Step by Step
By using the formula,
${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$
Where, $ n=10,r=4$
$\begin{align}
& {}_{10}{{P}_{4}}=\frac{10!}{\left( 10-4 \right)!} \\
& =\frac{10!}{6!}
\end{align}$
$\begin{align}
& =\frac{10\times 9\times 8\times 7\times 6!}{6!} \\
& =10\times 9\times 8\times 7 \\
& =5040 \\
\end{align}$
Thus, a president, vice president, secretary, and treasurer can be chosen in 5040 ways.
