13. Mr. Osterhold, the Physical Education teacher at Vista Virtual School, is having his PE20 class plan a floor hockey tournament. The class has been told they can invite other schools to play, and they can schedule 72 round-robin games in total with each team playing each other twice.

a. Determine the maximum number of teams that can enter the tournament. (1 mark)

b. Mr. Osterhold must pick three students from his PE20 class to present trophies to the top three-floor hockey teams in the tournament. There are 21 students in his class. Determine, as an exact value, the probability that Kelly and his two friends, Dom and Bryan, will hand out trophies to the winning teams. (2 marks)

c. Mr. Osterhold plays in a men's hockey league on Sunday nights. This year his team won 37% of their regular-season games, which was high enough for them to make it into the playoffs. Based on their past record, evaluate the probability of Mr. Osterhold's team losing their first game and winning their second game during playoffs, to the nearest percent. (2 marks)