A class has 12 students. In how many different ways can the students be put into groups of 3?

Answere is 369 600

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- Mar 3rd 2008, 02:08 PMwikjiData Help!!! Counting Techniques
A class has 12 students. In how many different ways can the students be put into groups of 3?

Answere is 369 600 - Mar 3rd 2008, 02:53 PMroy_zhang
Since the order of students within each group does not matter, we use combination as:

$\displaystyle \binom{12}{3}\binom{9}{3}\binom{6}{3}\binom{3}{3}= 369600$ - Mar 3rd 2008, 03:33 PMPlato
That is not the answer to the problem as it is stated.

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 $\displaystyle \frac{{\left( {12} \right)!}}{{\left( {3!} \right)^4 \left( {4!} \right)}}=15400$