Suppose that there are eight runners in a race. The winner receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. How many different ways are there to award these medals, if all possible outcomes of the race can occur and there are no ties?
Show Hint
Whenever positions, ranks, or medals are involved, order matters. Therefore use permutations:
\[
{}^nP_r=\frac{n!}{(n-r)!}.
\]
If order does not matter, use combinations instead.