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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 :

Cricetus

Answer:

The correct answer is "168 students".

Step-by-step explanation:

According to the question,

Graduation probability,

[tex]P_g=\frac{1}{4}[/tex]

Major probability,

[tex]P_m=\frac{1}{21}[/tex]

Now,

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

= [tex]\frac{1}{4}\times \frac{1}{21}[/tex]

= [tex]\frac{1}{84}[/tex]

hence,

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

⇒ [tex]\frac{x}{84}=2[/tex]

By applying cross-multiplication, we get

⇒ [tex]x = 84\times 2[/tex]

⇒    [tex]=168[/tex]

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