Explanation

(c)
Let there be $'n$’ men participants. Then, the number of games that the men play between themselves is 2. $\ ^{n}C_{2}$ and the number of games that the men played with the women is $2.(2n)$
$\therefore\ 2.{\ ^{n}C}_{2} - 2.2n = 66$ (given)
$\Rightarrow n(n - 1) - 4n - 66 = 0$
$\Rightarrow n^{2} - 5n - 66 = 0$
$\Rightarrow (n + 5)(n - 11) = 0$
$\Rightarrow n = 11$
$\therefore$ Number of participants =11 men+2 women=13