If there are 12 teams in a basketball tournament and each team must play every other team in the eliminations, how many elimination games will be?

In each game, the first team can be any one of the 12,

and the second team can be any one of the remaining 11.

Total number of ways to match them up = (12 x 11) = 132.

BUT ... Every game can be described as two different match-ups ...

either as ' A ' playing ' B', or as ' B ' playing ' A '.

Although there are 132 ways to make a match-up, every possible

pair of teams shows up twice in that list.

So in order for every team to play every other team, there are

only (132 / 2) = 66 different games required.