Part A) Of the $10$ kids in a chess club, $5$ are left-handed and $5$ are right-handed. The club holds a round-robin tournament in which every player plays against every other player exactly once. Of all the matches, how many of them have a left-handed player competing against a right-handed player?
Part B) Of the $10$ kids in a chess club, $5$ are left-handed and $5$ are right-handed. The club holds a round-robin tournament in which every player plays against every other player exactly once. Of all the matches, how many of them have a left-handed player competing against a right-handed player?
Part C) Of the $10$ kids in a chess club, $5$ are left-handed and $5$ are right-handed. The club holds a round-robin tournament in which every player plays against every other player exactly once. What fraction of the games have two right-handed players? Enter your answer as a fraction in simplified form.
