This will lead to duplication, because whether the teacher assigns first or later depends only on the final result, such as your method. If teacher 1 is assigned to class 1, no matter which time, A(3/5) or the second time, it is division. This is a combination problem, not an arrangement problem.

It can be calculated that the final score is 2 21. Choose one of the three classes and assign a teacher C(3/ 1). Assign one teacher to this class, and the remaining four teachers are assigned to two classes, with two teachers in each class. If graded, it is C(3/ 1).