Question

In a chess tournament, all participants were to play one game with the other. Two players fell ill after having played 3 games each. If total number of games played in the tournament is equal to 84, then total number of participants in the beginning was

(A)  10

(B)  15

(C)  12 

(D)  14

Answer 1

Correct option (B)  15

Let there were ‘n’ players in the beginning. Total number of games played in the tournament is ⁿC₂ and each player would have played (n – 1) games. Thus,

⇒  ⁿC₂ – ((n – 1) + (n – 1) – 1) + 6 = 84

⇒ n₂ – 5n – 150 = 0

⇒ n = 15