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?
There are 9 ways to choose a single person.
You then have \(8 \choose 4\) ways to choose a group of 4 people. But, you have to divide by 2, to correct for overcounting.
Once that is done, you have \({4 \choose 4} = 1\) way to choose the remaining.
Thus, there are \(9 \times {8 \choose 2} \div 2 = \color{brown}\boxed{315}\) ways.
All credit goes to Melody: https://web2.0calc.com/questions/a-group-of-nine-people-is-be-split-into-three-teams_1
We can choose any 4 of the 9 people to be on 1 of the 3 teams
And then we can choose any 4 of the 5 remaining people to be on 1 of the remaining 2 teams
The last person is on the last team by default
So
C ( 9,4) * C ( 3,1) * C(5,4) * C (2,1) = 3780 ways
Not totally confident about this, but BuiderBoy will probably have the correct answer !!!! (LOL !!! )
The answer isn't mine tho...
It's Melody's and I trust them more than I trust myself...