Question

Suppose that each student at a university has one of 4 expected graduation years and one of 21 majors. How many students must be enrolled to guarantee 2 graduations in the same year and major?

Answer 1

The correct answer is "168 students".

Explanation:

According to the question,

Graduation probability,

`P_g=(1)/(4)`

Major probability,

`P_m=(1)/(21)`

Now,

The probability of having both graduation as well as major will be:

=
`(1)/(4)* (1)/(21)`

=
`(1)/(84)`

hence,

The number of students having guarantee two graduations throughout the same year and major will be:

⇒
`(x)/(84)=2`

By applying cross-multiplication, we get

⇒
`x = 84* 2`

⇒
`=168`