A class has 12 students. In how many different ways can the students be put into groups of 3?
Answere is 369 600
That is the answer to this question: “A class has 12 students. In how many different ways can the students be put into teams of 3; a red team, a green team, a blue team, a brown team?” Someone might prefer being on the red team rather than being on a blue team. These are known as ordered partitions.
But that is not the question as stated.
This is like dividing the class into ‘study-groups’ where only content matters. These are known as unordered partitions.
The answer in this case is