six teammates are competing for first, second, and third place in a race. how many possibilities are there…

Explanation:

Step1: Use 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 $n = 6$ (the number of teammates) and $r=3$ (the top - three positions).

Step2: Calculate factorial values

$n!=6! = 6\times5\times4\times3\times2\times1=720$ and $(n - r)!=(6 - 3)!=3!=3\times2\times1 = 6$.

Step3: Compute the permutation

$P(6,3)=\frac{6!}{(6 - 3)!}=\frac{720}{6}=120$.

Answer:

C. 120