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MathNet 2012 Question 59

Math Olympiad Vault · MathNet 2012

Question 59

Four teams, including Quixajuba, play a volleyball tournament in which:
- Each team plays every other team exactly once.
- Every match ends with one team winning.
- In every match, the teams have equal chances of winning.
- At the end the teams are ranked by their number of wins.

a) Can all teams finish with the same number of wins? Why?

b) What is the probability that Quixajuba finishes alone in first place?

c) What is the probability that three teams finish tied for first place?