a group of campers is going to occupy 3 campsites at a campground. there are 16 campsites from which to…

a group of campers is going to occupy 3 campsites at a campground. there are 16 campsites from which to choose. in how many ways can the campsites be chosen? there are possible ways to choose the campsites.

a group of campers is going to occupy 3 campsites at a campground. there are 16 campsites from which to choose. in how many ways can the campsites be chosen? there are possible ways to choose the campsites.

Answer

Explanation:

Step1: Identify the combination formula

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here, $n = 16$ (total campsites) and $r=3$ (campsites to be chosen).

Step2: Calculate factorial values

$n!=16! = 16\times15\times14\times13\times\cdots\times1$, $r!=3!=3\times2\times1$, and $(n - r)!=(16 - 3)!=13!=13\times12\times\cdots\times1$. Then $C(16,3)=\frac{16!}{3!(16 - 3)!}=\frac{16!}{3!×13!}=\frac{16\times15\times14\times13!}{3\times2\times1\times13!}$.

Step3: Simplify the expression

Cancel out the $13!$ terms. We get $\frac{16\times15\times14}{3\times2\times1}=\frac{3360}{6}=560$.

Answer:

560