Question

Jenna is at a fair with four friends. They all want to ride the roller coaster, but only three people can fit in a car. How many different groups of three can the five of them make

Answer 1

They can make 10 different groups of three.

Explanation:

The order in which the people are in the car is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

How many different groups of three can the five of them make?

Combinations of 3 from a set of 5. So

`C_(5,3) = (5!)/(3!(5-3)!) = 10`

They can make 10 different groups of three.