H.15 Number of games of round-robin tournament

A league match (round-robin tournament) is held with 10 teams.

In case each team plays a match against other teams only once, how many games is it carried out in all?

Answer

45 games

Solution

Since ten team plays a match against 9 (10-1) teams once, the number of games will be 10 × 9 = 90 games. 

Games of A team vs B team and B vs A for example are double counting. 

Therefore total number of games is 90/2 = 45 games.