I think I have an approach to this one . . .Three friends and 17 other boys are to be randomly divided into five teams of 4 players.
Out of the total amount of teams, how many will have at least 2 of our friends
play for the same team?
ALL possible outcome total =
. Assuming the 5 teams are interchangeable, I agree!
The opposite of "at least two on the same team" is "none on the same team."
. . That is, the three friends are on separate teams.
In how many ways is this possible?
Call the friends
Place them in three different teams . . . it doesn't matter which teams.
The teams look like this:
The other 17 players will be partitioned into: 3, 3, 3, 4, 4.
Hence, there are: . .ways the friends are separated.
Therefore, the desired number is: .