Let the Games Begin!

April 23, 2018

This season, each team in the Davis City softball league will play each other team exactly once. If a total of 15 games will be played, how many teams are in the league?

 

The mayor’s two daughters each play for a different team in the Davis City softball league. This season, the mayor’s schedule will allow him to attend only one softball game. If he randomly selects which one of the 15 games to attend, what is the probability that the mayor will select a game in which at least one of his daughters is playing? Express your answer as a common fraction.

 

Next year, in order to extend the season beyond 15 games, after every team plays each other team once, the league will have every team play each other team a second time. If the order of the 15 games in the first half of the season and the order of the 15 games in the second half of the season are chosen at random, what is the probability that the two teams that play in the 1st game of the season will be the same two teams that play in the 30th game of the season? Express your answer as a common fraction.

 

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