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?
7 teams x 7 teams x 1 game = 49 games.
Then INTRA division 2 divisions each team of 7 must play 6 more teams TWICE 2 x 7 x 6 x 2 =168
168 + 49 games = 217 games (I think .............. )
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
Thanx , Chris ! Guess I should not have changed mt original answer......