In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is

The number of ways of allotment without any restriction is 8P6. Now, it is possible that none of the rooms of 2nd floor or 3rd floor are occupied. Thus, there are two ways in which one floor remains unoccupied. Hence, the number of ways of allotment in which a floor is unoccupied is 2 × 6! Hence, number of ways in which none of the floor remains unoccupied is 8P6 - 2(6!).