Subject: Circular Permutations
Who is asking: Student
Why not think about seating the women first, say in a cyclic order 1,2,3,4. I no woman sits adjacent to another then this defines 4 spaces between consecutive women for the men to be seated. Pick the first man, spouse of #1; in how many ways can he be seated? What about the second man, spouse of #2??
Two other situations are possible. The first is that exactly two women sit adjacent to each other and the second that there are two pairs of women who sit adjacent to each other. In both cases you can analyze how the men can be arranged.Cheers,