Official Guide Combination question

[tomintampa]

There are eight teams and each team plays each other exactly once. Each game is between 2 teams. What is the total number of games played?

The answer is 8C6 = 28. Why is it not 8C7? I'm confused and the official answer doesn't address combination theory at all. Thank you.

[saravanants]

The number of different ways 2 teams can be picked up from 8 is 8c2 = 8!/6!*2! = 56/2 = 28.

[venkpeters]

Another logical approach is each team will play with 7 other teams so total is 8*7 = 56 and out of 56 since a match involves 2 teams at once we can divide 56/2 = 28 matches overall

[GMATQuantCoach]

First of all 8C2 = 8C6. Basically nCk = nC(n-k).

I'm trying to understand your mistake 8C7. I'm not sure what you mean by that.

8C6 represents the # of ways to choose 6 teams that don't play while the 2 teams play.
Logically, this is same as choosing the 2 teams to play and leaving the 6 teams alone.

For example, when you need to choose a winner, you can choose him/her directly, or you can choose all the losers and leave the 1 left as your winner. In either way, you get your winner. Therefore nCk = nC(n-k)