Question

The number of volleyball games that must be scheduled in a league with n teams is given by G(n) = (n² - n)/2 where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?

Answer 1

Number of games = 15 

G(n) = (n² - n)/2 

By the given condition

(n² - n)/2 = 15

n² – n = 30 ⇒ n² – n – 30 = 0

(n – 6) (n + 5) = 0 

n – 6 = 0 or n + 5 = 0 

[Note: – 5 is neglected because number of team is not negative] 

n = 6 or n = -5 

∴ Number of teams = 6