Question

There are 15 students in the 8th grade. The students are randomly placed into three different algebra classes of 5 students each. Trevor, Terry and Evan are best friends. What is the probability that all three of them will be in the same algebra class?

Answer 1

The probability is
`(6)/(91)` ≅
`0.0659`

Explanation:

Let's analyze the question.

There are 15 students in the 8th grade.

The students are randomly placed into three different algebra classes of 5 students each.

We are looking for the probability that Trevor, Terry and Evan will be in the same algebra class.

One possible way to solve this question is to think about the product probability rule.

We can use it because we are in an equiprobable space. (And also the events are independent).

Let's set for example a class for Evan.

The probability that Evan will be in a class is
`1`

Then for Terry there are
`4` places out of
`14` that puts Terry in the Evan's class.

We write
`1.(4)/(14)`

Finally for Trevor there are
`3` places out of the remaining
`13` that puts Trevor in the same class with Evan and Terry.

Using the product rule we write :

`1.(4)/(14).(3)/(13)=(6)/(91)`

The probability of the event is
`(6)/(91)` ≅
`0.0659`