Question

there are 12 teams, each representing a different country, in a womens 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.
220
440
1,320
1,728

Explanation:

Step1: Identify permutation formula

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be selected. Here, $n = 12$ (number of teams) and $r=3$ (number of medals).

Step2: Calculate factorial values

$n!=12! = 12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, and $(n - r)!=(12 - 3)!=9!=9\times8\times7\times6\times5\times4\times3\times2\times1$. Then $P(12,3)=\frac{12!}{9!}=\frac{12\times11\times10\times9!}{9!}$.

Step3: Simplify the expression

Canceling out the $9!$ terms, we get $P(12,3)=12\times11\times10 = 1320$.

Answer:

C. 1,320