$\mathbf{\underline{Answer:\Rightarrow (b})}$
$\mathbf{\underline{Explanation:\Rightarrow }}$
As all the students are multi-talented, then we do want most of them to participate so as to maximize the gain, and also because each individual has the skills to take part in the subset of events.
So, we just have to calculate the maximum independent set for this problem where the nodes represent the events and edges represent the pair of events, when the above situation is represented graphically.