To determine how many ways you can divide 12 people into 3 teams of 4, we can follow these steps:
First, we calculate the ways to choose the first team of 4 from 12 people. This can be done using the combination formula:
C(n, k) = n! / (k!(n – k)!)
For the first team:
C(12, 4) = 12! / (4!(12 – 4)!) = 495
Now, we need to select 4 people for the second team from the 8 remaining people:
C(8, 4) = 8! / (4!(8 – 4)!) = 70
Finally, the last 4 people will automatically form the third team:
Now, we multiply the number of ways to select the first and second teams:
495 (first team) * 70 (second team) = 34,650
However, since the order of the teams doesn’t matter (i.e., Team A, Team B, and Team C are indistinguishable), we have overcounted the arrangements of the teams. There are 3! (6) ways to arrange 3 teams. Therefore, we need to divide by 6:
Total ways = 34,650 / 6 = 5,775
So, there are 5,775 different ways to split 12 people into 3 teams of 4.