Q. 1.23 - A First Course in Probability

Question

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?

Step-by-Step Solution

Answer

The possible number of assignments are $48$.

Step 1. Given information.

It is given that,

No. of rooms $=3$

No. of beds in each room $=2$

So, total number of beds $=3\times 2=6$

Step 2. Find possible number of assignments.

No. of ways to distribute $3$ pair of twins in $3$ rooms$=3!=3\times 2\times 1=6$

No. of ways to allocate bed to each twin $=2!=2\times 1=2$

Therefore, the possible number of assignments are $=6\times 2\times 2\times 2=48$.