There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrically situated (that is each room is exactly opposite to one other room). Four guests have to be accommodated in four of the eight rooms (that is, one in each) such that no two guests are in adjacent rooms or in opposite rooms. If $N$ is the number of ways in which guests can be accommodated. Then the value of $\frac{N}{6}$ is

Solution

Clearly guests will stay either in '✓' or in '×'



Therefore, number of required ways $=2\times 4!=48$ .

Hence, the correct answer is 8.