Four people, A$,$ B$,$ C$,$ and D$,$ are all looking to rent space in an apartment building. There are three floors in the building, $1,2,$ and $3($where $1$ is the lowest floor and $3$ is the highest$).$ Each person must be assigned to some floor, but it$$s ok if more than one person is living on a floor. We have the following constraints on assignments: