A group of nine people is be split into three teams, so that one team has four people, one team has three people, and one team has two people. How many ways can this be done?

wiskdls May 12, 2018

#1**+2 **

Hey wiskdls!

If there are 9 people in a group, there are \(\binom94\) = 126 ways to choose a 4 person group.

Since the 4 person group is already chosen, we have 5 people left.

To choose a 3 person group, we do \(\binom53\) = 10

Now there is 2 people left and to choose a 2 person group, there is only 1 way to do it.

\(126\cdot10=\boxed{1260}\)

Note: The order which you choose groups does not matter. You can first choose the 3 person group or first choose the 2 person group. The answer is still going to be 1260.

I hope this helped,

Gavin.

GYanggg May 12, 2018