Question

There are 12 contestants in a coloring contest. Three ribbons will be awarded. How many different ways could the ribbons be awarded?

Answer 1

1320 ways

Explanation:

Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.

The permutation formula is:

`_(n)P_(k)=(n!)/((n-k)!)`

n = 12

k = 3

Now that we have our variables, let's plug them into the formula.

`_(12)P_(3)=(12!)/((12-3)!)`

`_(12)P_(3)=(12!)/(9!)`

`_(12)P_(3)=1320`

So there are 1320 different ways that the contestants will be awarded.