Question

There are 12 teams, each representing a different country, in a women’s Olympic basketball tournament. In how many ways is it possible for the gold, silver, and bronze medals to be awarded? Use the formula for permutations to find your answer.

Answer 1

Answer:

1320 ways

Step-by-step explanation:

To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!

12! is the same as 12x11x10x9x8... etc

But in this problem, we are only looking for the top 3.

We can set up a formula

$\frac{n!}{(n-r)!}$

N is the number of options that are available and r represents the amount we are choosing

In this case, we have 12 teams so n=12

We are looking for the top 3 so r=3

$\frac{12!}{(12-3)!}$

$\frac{12!}{9!}$

We expand the equation and cancel out

$\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}$

Notice how both sides can cancel out every number 9 and below

That leaves us with 12x11x10

1320 ways