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

Answer:

They can make 10 different groups of three.

Step-by-step 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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

Combinations of 3 from a set of 5. So

$C_{5,3} = \frac{5!}{3!(5-3)!} = 10$

They can make 10 different groups of three.