Unlabeled Team Split

First count divisions into labeled teams, then correct for the fact that the teams are indistinguishable.

Divide by $3!$ to remove the overcounting from unlabeled teams.

1. 1. Labeled teams

   The number of ways to split 12 people into 3 labeled groups of 4 is $\frac{12!}{(4!{)}^3}$.

2. 2. Unlabel the teams

   Since the teams are indistinguishable, divide by $3!$ to avoid overcounting identical partitions.

   $$\frac{12!}{(4!{)}^{3}3!}$$

3. 3. Evaluate

   This equals $5775$.

Answer: 12! / ((4!)^3 * 3!)