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

Question

Four men and four women are to be seated alternately in a row. In how many ways can this be done ?

A. 288
B. 576
C. 864
D. 1152
E. 1728

CrackverbalGMAT · Answer

4 men and 4 women to be seated alternatively.

We can have men in the odd places and women in the even places: M W M W M W M W

Arrangements for Men = 4 * 3 * 2 * 1 = 24

Arrangements for Women = 4 * 3 * 2 * 1 = 24

Total arrangements for the above = 24 * 24 = 576

Similarly we can have 576 arrangements for women in the odd places and men in the even places: W M W M W M W M

Therefore total arrangements = 576 + 576 = 1152

OPTION D

Arun Kumar

wishmasterdj · Answer

Does this assume there cant be 9 seats in total?

If, after seating all women first (say), there should be 5 places for the men, so should it not be 4! * 5! ?

Fdambro294 · Answer

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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sanagupta · Answer

Bunuel  can you please explain why this is wrong?

Bunuel · Answer

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.

ishaanp2799 · Answer

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?

Regor60 · Answer

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.

Posted from my mobile device

ishaanp2799 · Answer

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

ShubhamA · Answer

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!
T otal - 8*3*2*1*4! = 1152 ways.

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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My Rewards