Question

a group of campers is going to occupy 4 campsites at a campground. there are 17 campsites from which to choose. in how many ways can the campsites be chosen?
there are \boxed{} possible ways to choose the campsites.

Explanation:

Step1: Identify the problem type

This is a permutation problem. 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 chosen. Here, \(n = 17\) (total campsites) and \(r=4\) (campsites to be occupied).

Step2: Calculate the factorial values

We know that \(n!=n\times(n - 1)\times\cdots\times1\). So, \(17! = 17\times16\times15\times14\times13!\) and \((17 - 4)!=13!\). Then \(P(17,4)=\frac{17!}{(17 - 4)!}=\frac{17!}{13!}\).

Step3: Simplify the expression

Since \(\frac{17!}{13!}=17\times16\times15\times14\) (the \(13!\) terms cancel out).

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Answer:

\(57120\)