Question 498179
Since all rooms are vacant 1st person can be placed in any of 4 rooms so 1st person can be placed in 4 ways

Now 1 room has been taken there left 3 vacant rooms, 2nd person can be placed in any of 3 rooms so 2nd person can be placed in 3 ways

Now 2 rooms have been taken there left 2 vacant rooms, 3rd person can be placed in any of 2 rooms, 3rd person can be placed in 2 ways

Now 3 rooms have been taken there left 1 vacant room, 4th person can be placed in remaining 1 room so 4th person can be placed in 1 way


Total number of ways = 4*3*2*1=24 ways


or 

make it more simple
4 persons can be placed in 4 rooms in = 4! ways =4*3*2*1=24 ways