Question

3. A psychology laboratory conducting dream research contains

3

rooms, with

2

beds in each

room. If

3

sets of non-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?

Answer 1

there are 3 rooms with 2 beds in each room

If there are 3 pair of IDENTICAL TWINS
Thee are 3! ways the pairs can be assigned rooms. In EACH room there are 2=2! ways the twins can be assigned beds and there are 3 rooms, hence you get 3 factors of 2!.
There are 6! possible sleeping arrangements in all,
so the probability of each pair sharing a room is (3!)(2!)(2!)(2!)/6! = 48

If there are 3 pair of NON-IDENTICAL TWINS
means they are just like 6 different people
so we need to choose 2 out of 6 in 6C2 ways = 15
again choose 2 out of 4 in 4C2 ways = 6
and 2 out of remaining 2 in 2C2 ways = 1

so we have 15*6*1 = 90 ways