Filling empty cells with random values from a list

Hello everyone.

I'm trying to fill in the empty cells randomly with a list of values, but these values cannot be duplicated on the same row and column, and can only be duplicated a set number of times.

I'll attach the sheet here.
I want to fill in the empty cells of the "Time/Teacher" table with the names from the "Student Name" list, but the student name cannot be duplicated within the same column and row, and can only be duplicated 5 times (# of classes)

Any advice would be greatly appreciated.