Question

A class of 6 boys and 12 girls are preparing for finals. The teacher is going to select 3 students to be exempt from the test. What is the probability that the three students that are exempt will be all boys?

Answer 1

`(5)/(204)`

Explanation:

Given:

In a class:

Number of boys = 6

Number of girls = 12

The teach has to select 3 students to be exempted from the test.

To find the probability that all boys students are exempted from the exam.

Solution:

Total number of students in the class =
`12+6=18`

Number of ways to select 3 students among 18 from the class can be given =
`18C3`

Total number of boys = 6

Number of ways to select 3 students among 6 boys can be given =
`6C3`

So, the probability of selecting all 3 students as boys can be given as =
`(6C3)/(18C3)`

⇒
`(6* 5* 4)/(3*2* 1)* (3*2*1)/(18*17*16)`

⇒
`(120)/(4896)`

⇒
`(5)/(204)` (Answer)