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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?

mathbum  Oct 4, 2018
 #1
avatar+13027 
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 cheeky.............. )

ElectricPavlov  Oct 4, 2018
edited by ElectricPavlov  Oct 4, 2018
edited by ElectricPavlov  Oct 4, 2018
 #2
avatar+89909 
+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

 

 

cool cool cool

CPhill  Oct 4, 2018
edited by CPhill  Oct 4, 2018
 #3
avatar+13027 
+1

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

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

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