A mathematics contest is held among four high schools. Each school enters a team

Question

A mathematics contest is held among four high schools. Each school enters a team on three students. The twelve contestants are ranked from 1 (best performance) to 12 (worst performance). The team that has the overall best performance (i.e., the lowest sum of ranks of the three students in the team) gets an award. In how many ways can the 12 ranks be assigned among the four teams without distinguishing between the individual ranks of the students in each team (since only the sum of their ranks matters)?

Explanation / Answer

The answer is 12!/(3!3!3!3!) since there are 12! ways of permutating the students and then we divide the number of ways by 3!^4 since there are 3! ways of permutating the 3 students in each of the four schools

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