TITLE: Arranging problem: 4 couples, 8 seats in a row... Am I making this too simple?
QUESTION [6 upvotes]: I am in a prob and stats course... haven't taken one in awhile and would like some help on these two problems.  I think I am probably making these a little two simple.  
Four married couples have bought 8 seats in a row for a concert.  In how many ways can they be seated if:
a. if each couple sit together?
4!2!2!2!2!= 384
b. if all men sit together?
I am thinking of this M1M2M3M4W1(Any women)(Any Women)(Any Women)(Any Women) so 4*3*2*1*4*3*2*1= 576

REPLY [2 votes]: a)  I think that answer is correct
b)The women can be arranged in 4! ways, the men can be arranged in 4! ways.
Then the men must be placed in one of the 5 following positions _ W _ W _ W _ W _   
$\therefore\,$ there are $4!*4!*5 = 2880$ ways all the men can sit together.