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. What fraction of the games are boy-versus-boy? Enter your answer as a fraction in simplified form.

Note: We need the number of girls and boys to calculate this question.

This is the application of combinations;

Suppose we have 6 boys and 6 girls participating in the tournament;

take C to represent the combination:

The total number of games = 12 C 2 = 66

only boys versus boys games = 6 C 2=15

only girls versus girls = 6 C 2=15

One girl versus one boy game=66-15-15=36

the fraction of the boys versus boys game = (total number of boys versus boys games) / (total number of games)

=15/66

=5/22

This methodology can be used to solve similar problems with different number of boys and girls participating in the tournament