Night reader wrote:Mark is a hotel administrator, and he is making room reservations for five participants of the Eurovision song contest. The number of rooms available for the participants is five on the fifth-room floor; the contest manager requires Mark to accommodate all participants so that no male participant's room neighbors other male participant's one. In how many ways can Mark arrange five rooms among three male and two female participants?

A. 24
B. 16
C. 12
D. 48
E. 30

Rahul@gurome wrote:This means that if the rooms are numbered 1 to 5, the males will occupy first, third and fifth rooms and the females will occupy second or fourth rooms.
The number of ways this can be done is 3!*2! = 12.
The correct answer is C.

Night reader wrote:
no male participant's room neighbors other male participant's one.