### Solution:

Let there be$\text{'}n\text{'}$ 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. $\left(2n\right).$

$\therefore $ $2.{}^{n}C_{2}-2n=66\Rightarrow {n}^{2}-5n-66=0\Rightarrow n=11.$

$\therefore $ Number of participants $=11$men + 2 women $=13.$