Answer
$15_{{P}{_{3}}}$ = 2730
Work Step by Step
Total number of flavors of ice cream = 15
Number of flavors used to create cones, with the position of them on top, middle ,and bottom is important = 3
To find the number of cones to create with three flavors of ice cream with the position of them on top, middle ,and bottom, we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)! }$
The number cones to create with three flavors of ice cream with the position of them on top, middle ,and bottom = $15_{{P}{_{3}}}$ = $\frac{15!}{(15 - 3)!}$
= $\frac{15!}{12!}$
= $\frac{15\times14\times13\times12!}{12!}$
= $15\times14\times13$
= 2730
