Five basket ball teams are playing in a tournament. the teams will play with each other only one time. how many games will be play by the end of the tournament?

Ten games will be played.

The first team can be any one of 5 .  For each of those, the opponent can be any one of the other 4 .

Number of ways to pair them up = (5 x 4) = 20 ways .

BUT ... Whether the Reds play the Blues, or the Blues play the Reds, it's the SAME GAME.  Each possible game shows up twice in the list of 20 ways.  So there are really only 10 different pairs ==> 10 games .