There are six professors teaching the introductory discrete mathematics class at someuniversity. The same final exam is given by all five professors. The exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible). How manystudents must there be to guarantee that there are two students with the same professorwho earned the same final examination score?

Question

Mathematics

Jesus Compton

9 January, 22:16

There are six professors teaching the introductory discrete mathematics class at someuniversity. The same final exam is given by all five professors. The exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible). How manystudents must there be to guarantee that there are two students with the same professorwho earned the same final examination score?

+2

Answers (1)

Know the Answer?

Ali Paul · Answer 1

607 students to guarantee that there are two students with the same professorwho earned the same final examination score.

Step-by-step explanation:

This problem is an example of the Pigenhole principle.

The first step is finding the number of boxes and objects:

For each score, we have a box which contains the student who got that score.

If there were only one professor grading, there would need to be 101+1 = 102 students to ensure that that there are two students with the same professorwho earned the same final examination score.

However, for each student, there are a combination of six to five = 6 possible combinations for a score.

So there should be at least 6*101+1 = 607 students to guarantee that there are two students with the same professorwho earned the same final examination score.