A) 6
B) 11
C) 13
D) None of these
Correct Answer: C
Solution :
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 \[2.\ (2n)\]. \[\therefore \]\[2.{{\ }^{n}}{{C}_{2}}-2\ .\ 2n=66\] (By hypothesis) \[\Rightarrow \]\[{{n}^{2}}-5n-66=0\Rightarrow n=11\] \[\therefore \] Number of participants\[=11\ \text{men}+2\ \text{women}=13\].
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