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

Answer:

1320 ways

Step-by-step 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:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$

n = 12

k = 3

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

$_{12}P_{3}=\dfrac{12!}{(12-3)!}$

$_{12}P_{3}=\dfrac{12!}{9!}$

$_{12}P_{3}=1320$

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