A group of nine people is be split into three teams, so that one team has four people, another team has four people, and the final team has one person. How many ways can this be done?
I think that there are 9 ways to chose the 1
then there are 8C4 ways to choose 4.
But each time you choose 4 you are also choosing the other 4 in the last group so my best guess is
9* 8C4 divided by 2
=9* 70 /2
= 315 ways.
choose 4 people from the 9 9 C 4 = 126
now choose 4 people from the remaining 5 5 C 4 = 5
and there is one left
126 x 5 x 1 = 630 ways
You have doubled counted.
Say the people are
Say you chose J as the single person then you chose A,B,C,D for the first group and then you are left with E,F,G,H for the last group.
this is the same as
............Chose J as the single person then you chose E,F,G,H for the first group and then you are left with A,B,C,D for the last group.
I am pretty sure my answer is correct.