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Question: 36 games were played at a chess tournament with each contestant playing once against each of the contestants. How many participants were there?


A ) 18
B ) 9
C ) 12
D ) 36
E ) 8

Steps to derive

1 Let the number of participants in the chess tournament = n.

2 The number of games played = 36

3 nC2 = 36

4 n!(n-2)!×2! = 36
 [nCr = n!(n-r)!×r! .]

5 n(n-1)(n-2)!(n-2)!×2! = 36
 [n! = n(n - 1)(n - 2)!.]

6 n2 – n = 72
 [Simplify.]

7 n2 – n – 72 = 0

8 (n – 9)(n + 8) = 0
 [Factor.]

9 n = 9, - 8

10 The number of players in the chess tournament = 9.
 [As n value cannot be negative.]



Hence the right answer is Option B

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