I have $n$ people each of which can meet on certain days of the week. I want to group them into $\frac{n}{k}$ groups of size $k$ such that all people in a group can meet on a day.
eg - Suppose there are 3 people who are free on (M,T,W,Th,F), (M,W) and (W,Th,F) respectively. They can all be placed in the same group since all of them can meet on Wednesday.