+0

yes

-1
490
3
+105

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?

Oct 4, 2018

#1
+18439
0

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 .............. )

Oct 4, 2018
edited by ElectricPavlov  Oct 4, 2018
edited by ElectricPavlov  Oct 4, 2018
#2
+101786
+3

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

Oct 4, 2018
edited by CPhill  Oct 4, 2018
#3
+18439
+1

Thanx , Chris !   Guess I should not have changed mt original answer......

ElectricPavlov  Oct 4, 2018
edited by ElectricPavlov  Oct 4, 2018