Four men and four women are to be seated alternately in a row. In how

Only 2 ways the Men and Women can be arranged alternately in a straight line:

Case 1: men take the odd places and women take the even places

M - F - M - F - M - F - M- F


Or

Case 2: women take the odd places and men take the even places

F - M - F - M - F - M- F - M


For each case, the no of arrangements possible is the same value.


The men can be arranged among their 4 chosen seats in 4! Ways

AND

The women can be arranged among their 4 chosen seats in 4! Ways


Case 1: 4! * 4!

Or

Case 2: 4! * 4!


= 4! * 4! + 4! * 4!

= (2) * (4! * 4!)

= (2) * (24 * 24)

= 1,152

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Bunuel can you please explain why this is wrong?

I'm not entirely clear on that doubt.

There are eight individuals involved: four men and four women. They must be seated alternately in either of these sequences: M - F - M - F - M - F - M - F or F - M - F - M - F - M - F - M. Each arrangement can be achieved in 4!*4! ways, leading to a total of 2*4!*4! = 1152 ways.

Answer: D.

­If I seat the men first in 4! ways: _ M _ M _ M _ M _ 


There are 5 seats vacant where we need to seat the remaining 4 women,

I choose those seats in 5C4 ways and then arrange them in 4! ways.

My answer becomes 4! * 5C4 * 4! = 2880 

Check this logic please?


 

This would allow men and women NOT to seat alternately, a requirement of the question, because any one of the three seats between men is unfilled in certain of the permutations, leaving two men to sit next to each other.

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­https://gmatclub.com/forum/in-how-many-ways-can-4-men-and-4-women-be-seated-in-a-row-such-that-no-397954.html

Posting this question for everyones reference:

This questions clearly states "seat them alternatively", while the question link I have posted states "no 2 women are to be seated together".

The latter has more possible arrangements, because there are fewer restrictions in the sense that 2 men can typically sit with an empty seat between them while maintaining the asked restriction of "No 2 women together." ->FMFM_MFMF this arrangement is possible here but is not in this given question. Refer below:

But in this particular question, there cannot be empty seats between anyone as they have to more rigidly sit exaclty alternatively, in the form FMFMFMFM OR MFMFMFMF

First Man/ Women has an option of choosing seat - 8 ways.
then 2nd man/woman has- 3 ways
3rd man/ woman - 2 ways
and 4th - 1 way.
i.e. 8*3*2*1

now, 4 seats are occupied. For remaining 4 seats, options left - 4!
Total - 8*3*2*1*4! = 1152 ways.