If eight basketball teams participate in a tournament, find the number of different ways that first, second, and third places can be decided assuming that no ties are allowed.

We are given 8 teams (objects) to arrange them in 3 places in different ways. We are asked to calculate the permutations of 8 different things taken 3 at a time. This will be given by : $$ ^8P_3=\frac{8^{}!}{\left(8-3\right)!}=\frac{8!}{5!} $$ $$ =8\times7\times6 $$ $$ =336 $$ So, we can arrange the 8 teams in 336 different ways to 1st, 2nd and 3rd position.