A sports conference has 14 teams in two divisions of 7. How many games are in a complete season for the conference if each team must play every other team in its own division twice and every team in the other division once?
Here's my attempt at this.....
For the in-divisional games we can choose any 2 of 7 teams in any division = (7, 2) = 21 unique pairings
Since each unique pair plays twice....this gives 2 * 21 = 42 games played within one division
And since there are 2 divisions...this gives us 2 * 42 = 84 in-divsional games
And since every team in plays every team in the other divsion once this gives us 7 * 7 = 49 more games
So...the total games played are 84 + 49 = 133 games