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(B) Let the number of men be $n$. Each participant plays $2$ games with every other participant. The number of games played between men is $2 	imes \

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(B) Let the number of men be $n$. Each participant plays $2$ games with every other participant. The number of games played between men is $2 	imes \binom{n}{2} = 2 	imes \frac{n(n-1)}{2} = n(n-1)$. The number of games played between men and women is $2 	imes (n 	imes 2) = 4n$. According to the problem,$n(n-1) - 4n = 66$. $n^2 - n - 4n = 66 \Rightarrow n^2 - 5n - 66 = 0$. $(n-11)(n+6) = 0$. Since $n$ must be positive,$n = 11$. Total participants = $n + 2 = 11 + 2 = 13$.

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