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Question
The number of volleyball games that must be scheduled in a league with n teams is given by G(n) = `("n"^2 - "n")/2` where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?
Solution
Number of games = 15
G(n) = `("n"^2 - "n")/2`
`("n"^2 - "n")/2` = 15
n2 – n = 30
⇒ n2 – n – 30 = 0
⇒ n2 – 6n – 5n – 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
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