Thread: Ordered Partition

I have this math problem that drives me absolutely nuts. I saw this same one at high school and again in college. Here it is:

In how many ways can 9 students be divided into three teams?

The answer to this question is

At high school, I asked my teacher why the answer being it is. He asked me to consider myself a coach. By so, I appoint a student for a team captain for each team and have each team captain choose two others for her team. When I said, "If I were the coach, why can't I choose them myself?" He was speechless.

Now I see this same problem again in a different book that gave the answer in this form:

I understand this part: , but I don't understand why it's multiplied by

Can anyone explain?

If you were to gave a RED team, a BLUE team and a GREEN team then would be correct.
That is because the color team can make a difference. I don’t want to be on the BLUE team.

But because there is nothing to distinguish the teams we divide by another .

If you want to divide twenty people into four groups of five each the number is .

Originally Posted by Plato

If you were to gave a RED team, a BLUE team and a GREEN team then would be correct.
That is because the color team can make a difference. I don’t want to be on the BLUE team.

But because there is nothing to distinguish the teams we divide by another .

If you want to divide twenty people into four groups of five each the number is .

Is in the denominator meant to get rid of the order:
{RED, BLUE, GREEN} {RED, GREEN, BLUE} {GREEN, BLUE, RED} {GREEN, RED, BLUE} {BLUE, GREEN, RED} {BLUE, RED, GREEN}=3!

Originally Posted by novice

Is in the denominator meant to get rid of the order:

Yes, in general.
Study the other example I gave you.

Originally Posted by Plato

Yes, in general.
Study the other example I gave you.

Thank you, Plato,
Now I don't have to get up in the middle of the night banging my head.