Answer
$31_{{P}{_{3}}}$ = 26970
Work Step by Step
Total number of different flavors of ice cream = 31
Number of flavors in a bowl = 3
To find the number bowls containing three different flavors of ice cream, we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)! }$
The number of bowls containing three flavors of ice cream = $31_{{P}{_{3}}}$ = $\frac{31!}{(31 - 3)!}$
= $\frac{31!}{28!}$
= $\frac{31\times30\times29\times28!}{28!}$
= $31\times30\times29$
= 26970
