## Precalculus (6th Edition) Blitzer

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.