Question

A group contains fi…ve men and fi…ve women. How many ways are
there to arrange these people in a circular table with ten seats if men and women alternate,
and the seatings are considered the same if each person has the same right neighbor and
left neighbor?

Answer 1

I would think of it as a line of people, rather than a circle.

m1, f1, m2, f2, ... m5, f5
This is the same as:
f5, m1, f1, m2, f2, ... m5

So basically, for every assignment, there are 10 redundant versions of it.

Answer 2

Now, to find the assignments, you'd have:
5m, 5f, 4m, 4f, ... 1m, 1f.

In other words, you'd have: 5! * 5! main assignments.

Answer 3

So I'm getting: 5! * 5! / 10