There are girls and boys in a chess club. The club holds a round-robin tournament in which every player plays against every other player exactly once.
If Anita is one of the club members, what fraction of all games at the tournament does Anita play in? Enter your answer as a fraction in simplified form.
Suppose there are n players in total. Then Anita plays n-1 other players. Each member plays n-1 other players, so it might seem as though there are n(n-1) games in total.
However, each game involves two players, so to avoid double counting we have to divide by 2 to get the total number of games as n(n-1)/2.
The fraction of games played by Anita is therefore (n-1)*2/(n(n-1)) → 2/n