Problem:
There are $12$ players in a sport. In how many ways can those students be partitioned into teams A, B and C such that the team size is $4$ students.
Answer:
There was some confusion about this between my teacher and me. I was left a bit unsure, but Grimaldi's discrete math textbook does present a similar problem with example answer also...
1.) My original answer is: $C(12,4) \cdot C(8,4) \cdot C(4,4) = 34650$
2.) My teacher thinks that the answer should be divided by ($3! = 6$)
3.) Grimaldi himself (the mathematician, author) apparently seems to think that it doesn't have to be divided by anything.
Grimaldi's book has similar problem written as "There are $36$ girls in volleyball P.E. class, and the teacher must divide the girls to teams of $9$. In how many ways can the teacher select teams A,B,C,D" Grimaldi's answer $= C(36,9) \cdot C(27,9) \cdot C(18,9) \cdot C(9,9)$ No division required!?!?!
This is some funky mathematics going on in here!