In a sports league, there are 20 total teams, divided into 4 divisions of 5 teams each. Over the course of a season, each team plays each of the other teams in its own division 3 times, and each of the other teams in the other divisions twice. How many games does the league have in a complete season?
I ended up getting $4(3{\binom{5}{2}}) + 2{\binom{4}{2}}({\binom{10}{2}} – 2{\binom{5}{2}})$, which evaluates to 420. Is this correct?
Best Answer
Yes, this is correct. First part is the games on own division and other parts is 2 games, you choose the two divisions and you choose one team of each division. So $$4\cdot 3\cdot \binom{5}{2}+\binom{4}{2}\binom{5}{1}\binom{5}{1}\cdot 2=420.$$