Question

A group of campers is going to occupy 3 campsites at a campground. There are 17 campsites from which to choose. In how many ways can the campsites be chosen?

Answer 1

Answer:

Campsites be chosen in 680 ways.

Step-by-step explanation:

Given:

Number of  campsites= 17

Number of campsites that are to be occupied=3

To Find:

Number of ways can the campsites be chosen=?

Solution:

Combination:

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!

No of ways in which campsites can be chosen= $\frac{17!}{3!(17-3)!}$17C3

=>$\frac{17!}{3!(14!)}$

=>$\frac{15\times16\times17}{3\times 2\times 1}$

=>$\frac{4080}{6}$

=>680