In a course, a professor gives five grades {A, B, C, D, F}. What is the minimum number of students required so that four of them are guaranteed to get the same grade?

In a course, a professor gives five grades {A, B, C, D, F}. What is the minimum number of students required so that four of them are guaranteed to get the same grade? Correct Answer 16

The correct answer is option 3.

Concept:

The pigeonhole principle states that if items are put into containers, then at least one container must contain more than one item.

Pigeonhole Principle:

If n pigeonholes are occupied by n+1 or more pigeons, then at least one pigeonhole is occupied by greater than one pigeon. Generalized pigeonhole principle is: - If n pigeonholes are occupied by kn+1 or more pigeons, where k is a positive integer, then at least one pigeonhole is occupied by k+1 or more pigeons.

The given data,

A professor gives five grades {A, B, C, D, F} n=5

Get the same grade k+1 =4

k=3

The minimum number of students=?

The minimum number of students= Kn+1

The minimum number of students= 3 x 5+1

The minimum number of students= 16

Hence the correct answer is 16.