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= [tex]\frac{17!}{3!(17-3)!}[/tex]17C3
=>[tex]\frac{17!}{3!(14!)}[/tex]
=>[tex]\frac{15\times16\times17}{3\times 2\times 1}[/tex]
=>[tex]\frac{4080}{6}[/tex]
=>680
