So, we are given rooms with beds like below
We have 3 pair of twins, So we can arrange them in rooms in 3! = $6$ ways
Let us call the twins in pair as Twin-A, Twin B
So, each pair of twins can be further arranged in 2 ways in a single room
- Twin-A on Left, Twin-B Right bed
- Twin-A on Right, Twin-B Left bed
Let us say one arrangement of twins in rooms is TwinSet 1 in Room 1, TwinSet 2 in Room 2, TwinSet 3 in Room 3
So, possible arrangements within rooms can be
Room 1 |
Room 2 |
Room 3 |
1 |
2 |
1 |
2 |
1 |
2 |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin B |
Twin A |
Twin A |
Twin B |
Twin B |
Twin A |
Twin A |
Twin B |
Twin A |
Twin B |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
Twin A |
Twin B |
Twin A |
Twin B |
Twin B |
Twin A |
Twin A |
Twin B |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
Twin A |
Twin B |
Twin B |
Twin A |
Twin B |
Twin A |
Twin B |
Twin A |
So, within each arrangement of twins in rooms, they can further be arranged in 2 x 2 x 2 = 8 ways
So, in 6 arrangements in rooms, the twins can be arranged in rooms in 8 ways
Total ways = 6 * 8 = 48 ways