A math contest is held among 4 middle schools. Each school enters a team of 3 students. The 12 contestants are ranked from 1 (best performance) to 12 (worst performance). The team that has the overall best performance (the lowest sum of the ranks of each team's students) gets an award. In how many ways can the 12 ranks be assigned among the 4 teams without distinguishing between the individual ranks of the students in each team (since only sum of rankings matters)?
Since the students from each team are identical, lets name them as A, A, A, B, B, B, C, C, C, D, D, D. Now arranging these 12 students in can be done in 12!/(3!)^4.