HCU MCA 2013 Paper

Question : 7 of 75

Marks: +1, -0

There were two women amongst other men who took part in a chess tournament. Every participart played two games with every other participart. The number of games which only men played was exactly 104 games more than those played which involved a women. The total number of participarts is

Validate

Solution:

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;2 (^\n \C_{2}) = 104 + 2 (^\n \C_{1})\;(^\2 \C_{1})

⇒

\;\;\;\;\;\;\;\;\n ( \n - 1) = 104 + 4\n

⇒

\;\n^2 - 5 \n - 104 = 0

⇒

{(\n-13) (\n + 8) = 0

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;n = 13

(∴ n cannot be negative)

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