In a class tournament where the participants were to play one game with one another, two of the class players fell ill, having played 3 games each. If the total number of games played is 27 , then the number of participants at the beginning was

Step-by-step solution

Suppose, the two players did not play at all such that the remaining n - 2 players played n - 2 C 2 matches. Since, these two players played 3 matches each, hence the total number of matches is n - 2 C 2 + 3 + 3 = 27 ⇒ n - 2 C 2 = 21 n - 2 C 2 = 21 ⇒ n - 2 n - 3 2 = 7 × 6 2 ⇒ n - 2 = 7 ⇒ n = 9 .