Question

There are 10 students in a class: 6 boys and 4 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

Answer 1

`(1)/(6)`.

Explanation:

It is given that,

Total number of students = 10

Number of boys = 6

Number of girls = 4

Total number of ways to select 3 students from 10 students.

`^(10)C_3=(10!)/(3!(10-3)!)=(10* 9* 8* 7!)/(3* 2* 1* 7!)=120`

Total number of ways to select 3 students from 6 boys.

`^(6)C_3=(6!)/(3!(6-3)!)=(6* 5* 4* 3!)/(3* 2* 1* 3!)=20`

The probability that everyone in the group is a boy is

`P=\frac{\text{Total number of ways to select 3 students from 6 boys}}{\text{Total number of ways to select 3 students from 10 students}}`

`P=(20)/(120)`

`P=(1)/(6)`

Therefore, the required probability is 1/6.