Answer
The number of possible bowls of different flavors of ice cream is $4,495$
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=31 \\
& r=3
\end{align}$
Then, we have to find the number of permutations of 31 things taken 3 at a time:
$\begin{align}
& {}_{31}{{C}_{3}}=\frac{31!}{3!\left( 31-3 \right)!} \\
& =\frac{31!}{3!28!} \\
& =\frac{31\times 30\times 29\times 28!}{6\times 28!} \\
& =4,495
\end{align}$
