Let number of teams participated in the tournament are n then, number of game played by, first team = (n – 1) Second team = (n – 2) ............................ ............................ ............................ (n – 1)th team = 1 According to the questions, (n – 1) + (n – 2) + (n – 3) +.....+ 1 = 45 This is equivalent to, selection of two ‘teams’ out of n teams nC2 ∴ nC2 = 45 ⇒