Question

There are 3 rooms in a flat and 2 people want to stay in it. Find the number of ways in which they can accommodate the rooms such that each room is occupied by only one person at a time?

Answer 1

There are 6 ways....When a person occupied atleast one room at a time

Answer 2

There will be total 6 ways of occupying room.

First Number the room such as A1, A2 and A3. Now the two people will occupy the room in a following way-

First person can occupy the room A1, A2 or A3 in a similar way second person can also occupy in A1 or A2 or A3. So when any two rooms are occupied by these two people the number of ways will be like this- A1A2, A1A3, A2A1, A2A3, A3A1 and A3A2.

We can calculate as 3 room X 2 person = 6 ways