1,947 views
2 votes
2 votes
A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3 sets of identical twins are to be assigned to these 6 beds so that each set of twins sleeps in different beds in the same room, how many assignments are possible?

each set of twins sleeps in different beds in the same room hence each twin assigned one room, here 3 twins and we arrange them into 3 rooms so 3! ways
twins are identical so no need of arranging them
so answer is only 3!=6

but given answer is 48

1 Answer

Best answer
4 votes
4 votes

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

selected by

No related questions found