How many ways can 8 people be seated in a row? I am stuck with the following question,

How many ways can 8 people be seated in a row?
  if there are 4 men and 4 women and no 2 men or women may sit next to each other.

I did it as follows,
As 4 men and 4 women must sit next to each other so we consider each of them as a single unit.
Now we have we 4 people(1 men group, 1 women group, 2 men or women) they can be seated in 4! ways.Now each of the group of men and women can swap places within themselves so we should multiply the answer with 4!*4! 
This makes the total  4!*4!*4! =13824 .
Please help me out with the answer. Are the steps clear and is the answer and the method right?
Thanks

Is it that no two men and no two women should be seated together. 
Yep? Then do this..
Permutation of men in 4 places be 4!. This leaves us with 5 gaps(3 in between and 2 on either side) in which we got to arrange 4 women.. P(5,4) i.e. 5! ways.
Finally   5!*4! is the answer!. 
