I need the solution to this problem to be able to resolve a situation at work. I believe some probability equation must be involved.

Problem:

There are 60 math teachers at a math competition conference meeting. All 60 teachers are asked to take the same math test to compare average score results. Unfortunately, there is no one else available to be grading all the tests so the teachers have to grade the tests themselves.

To eliminate any kind of margin of error, each teacher is asked to grade 20 tests of their peers, selected at random. Each graded test corresponds to one score. At the end, the teacher's final score for the test will be equal to the average of all the scores that have been graded from the other teachers.

How many scores will each teacher receive if all 60 teachers grade 20 tests of their peers selected at random?