In a football championship, there are 15 matches. If each team plays one match with every other team, the number of teams is-

Question: In a football championship, there are 15 matches. If each team plays one match with every other team, the number of teams is-

Solution:
Let n be the number of teams.
ⁿC₂ = 15
⇒ n!/{2! × (n - 2)!} = 15
⇒ {n(n - 1)(n - 2)!}/{2! × (n - 2)!} = 15
⇒ n(n - 1)/2 = 15
⇒ n(n - 1) = 30
⇒ n2 - n - 30 = 0
⇒ n - 6n + 5n - 30 = 0
⇒ n(n - 6) + 5(n - 6) = 0
⇒ (n - 6)(n + 5)
∴ n = 6 [Negative value is not acceptable]