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?

The correct answer is "168 students".

Step-by-step explanation:

According to the question,

Graduation probability,

Major probability,

Now,

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

=

=

hence,

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

⇒

By applying cross-multiplication, we get

⇒

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