#### Answer

The number of cones that can be formed with three different flavors from 15 total flavors is $2730$.

#### Work Step by Step

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:
$\begin{align}
& {}_{15}{{P}_{3}}=\frac{15!}{\left( 15-3 \right)!} \\
& =\frac{15!}{12!} \\
& =\frac{15\times 14\times 13\times 12!}{12!} \\
& =2,730
\end{align}$