Hello.

I am not too sure how to start this one.

Q: 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 = $\displaystyle {20\choose4,4,4,4,4} / 5!$

Also, is the division by 5! to negate the need of order? Because I originally thought that the $\displaystyle {20\choose4,4,4,4,4}$ would be the total result.

Anyways, I was thinking of starting the question something like this.

$\displaystyle {19\choose4} * {16\choose4,4,4,4} /5!$

Does this sound about right? Thanks for any help, much appreciated.