Question

There are 5 cyclists in a race. If the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal, how many different permutations are possible for the medal winners?

Answer 1

`60`.

Explanation:

Here, the order would matter, so we use the permutation formula.

The permutation formula is `color(white)(2)_nP_r = (n!)/((n - r)!)`, where `n` is the total number of elements (5) and `r` is the number being picked (3).

`color(white)(2)_5P_3 = (5!)/((5 - 3)!) = (5!)/(2!) = (5 * 4 * 3 * 2 * 1)/(2 * 1) = 5 * 4 * 3 = 60`

Therefore, there are `60` possible permutations.

Hopefully this helps!