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,
a) how many assignments are possible?
b) which is the probability of that every set of twins sleep in the same room?
In a) I know that are $(3!)(2!)(2!)(2!)=48$, but I don't understand why.
For b), I don't know how to proceed. Any help will be appreciated!
$\endgroup$1 Answer
$\begingroup$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!. Does that help? for b. There are 6! possible sleeping arrangements in all,so the probability of each pair sharing a room is (3!)(2!)(2!)(2!)/6!
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