Bunuel wrote:

sarb wrote:

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15

B. 16

C. 28

D. 56

E. 64

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\).

Answer: C.

P.S. Please read and follow:

http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention ot the points #3 and #8.

Bunuel you know I got confused by your shortcut solution

until figured out all possible combinations in details . you know what surprises how this expression \(C^2_{8}=28\)

excludes the possibility of playing more than one game by two distinct teams, also it exludes repeated games like AB and BA....

let 8 teams be A, B, C, D, E, F, G, H

NUMBER OF GAMES PLAYES BY TWO TEAMS AS FOLLOWS:

AB BC CD DE EF

AC BD CE DF EG

AD BE CF DG EH

AE BF CG DH

AF BG CH

AG BH

AH

niks18 your comments are always appreciated

have a great day

_________________

In English I speak with a dictionary, and with people I am shy.