Hello, chrisc!

IThree 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!thinkI have an approach to this one . . .

The opposite of "at least two on the same team" is "none on the same team."

. . That is, the three friends are onseparateteams.

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: .