The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
For each division, there are 6 choose 2, or 6(5)/2, or 15 ways to pair up two teams. Since each pair plays twice, that means 30 games within each division. So there are 6(6), or 36 cross-division games. Adding up these two types of games, I get 30 + 30 + 36, or 96 conference games in total. 