Question

A certain class has 11 students, 6 boys, and 5 girls, and they have no matched birthdays. What is the probability that 3 eldest students are all boys?

Answer 1

`(4)/(33)`.

Explanation:

Given information:

Total number of students = 11

Number of boys = 6

Number of girls = 5

It is given that they have no matched birthdays.

We select 3 eldest students. So, the total number of ways are

`^(11)C_3=(11!)/((11-3)!3!)=165`

Possible ways of selecting 3 eldest students are all boys.

`^(6)C_3=(6!)/((6-3)!3!)=20`

So, the probability that 3 eldest students are all boys is

`P=(20)/(165)=(4)/(33)`

Therefore, the required probability is
`(4)/(33)`.