School board member A prefers football to basketball and basketball to synchronized swimming. Member B prefers basketball to synchronized swimming and synchronized swimming to football. Member C prefers synchronized swimming to football and prefers football to basketball.

a)The nonvoting chairperson indicates the that the district can afford to hire one coach only and proposes a vote determining whether to hire a basketball or football coach. Which will be hired?

b)If later, as funds become more available, the chair proposes a vote between hiring a synchronized swimming coach or a basketball coach, which coach does the district hire?

c)If the chair had initially in the first vote proposed a vote between football and synchronized swimming, which coach would the district have hired?