Answer
$3360.$
Work Step by Step
Apply the Fundamental Principle of Counting
If $n$ independent events occur, with $m_{1}$ ways for event 1 to occur,
$m_{2}$ ways for event 2 to occur,
$\ldots$ and $m_{n}$ ways for event $n$ to occur,
then there are $m_{1}\cdot m_{2}\cdot\cdots\cdot m_{n}$ different ways for all $n$ events to occur.
---
$m_{1}=16$ ... 16 desserts to choose from, for 1st place
$m_{2}=15$ ... of the 15 remaining, one will have won 2nd place
$m_{3}=14$ ... of the 14 remaining, one will have won 3rd place
Total = $16\times 15\times 14$ = $3360.$
Another approach:
Permutations, r=3 taken from n=16:
$P(n,r)=\displaystyle \frac{n!}{(n-r)!}=\frac{16\times 15\times 14\times 13!}{(16-3)!}$=$16\times 15\times 14$
