Combinatorics question

[sherifabdulla]

Hi

Can somebody please help me tackle this combinations question using the adjacent method:

If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?

My thinking was:
There are 10 seats, where you can fit 5Ms and 5Ws. Therefore 10 lines:
_ _ _ _ _ _ _ _ _ _

But every M must be next to a W, so if I take "MW" as one element. There you can think of it as five lines each fitting an "MW":
__ __ __ __ __

That gives us 5! combinations of MWs

But we also need to account for the total number of MW elements you can create. That's 5!

So that's 5!5! (i.e. for every possible set of MW combinations, there are 5! arrangements)

But we also need to account for "WM" elements, so we multiply by 2!

That gives us 5!5!2!

Which is incorrect. Can somebody please explain to me the flaw in my reasoning?

Thanks!

[RonPurewal]

Per the forum rules, please provide the following:

* A citation of the original source of the problem (not another forum"”we need original authorship / identity of the copyright holder)

* The full text of the problem

* All answer choices that accompany the problem in its original formulation

Thanks.