## Precalculus (6th Edition) Blitzer

The number of cones that can be formed with three different flavors from 15 total flavors is $2730$.
We know that: ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ So, from the information, \begin{align} & n=15 \\ & r=3 \end{align} Then, we have to find the number of permutations of 15 things taken 3 at a time: \begin{align} & {}_{15}{{P}_{3}}=\frac{15!}{\left( 15-3 \right)!} \\ & =\frac{15!}{12!} \\ & =\frac{15\times 14\times 13\times 12!}{12!} \\ & =2,730 \end{align}