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# In how many ways can 4 men and 4 women sit at a round table

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Director
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In how many ways can 4 men and 4 women sit at a round table [#permalink]

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06 Jan 2005, 10:52
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In how many ways can 4 men and 4 women sit at a round table with no two women in consecutive postions?
A) 24
B) 72
C) 288
D) 144
E) 48
Director
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07 Jan 2005, 12:25
Can somebody try to answer this pl...

I am bumping this up to get more attention
Director
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07 Jan 2005, 12:29
I think its D.

The only way for two women to not sit in consecutive positions would be for them to alternate with a man. So, it would be 4! * 3! = 24*6= 144.

Similar to the prolem discussed here...
http://www.gmatclub.com/phpbb/viewtopic.php?t=12879
Director
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07 Jan 2005, 12:45
Thanks swath20 and gayathri.
You got it right.
Thanks for the link to understand the concepts behind such problems.
Current Student
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07 Jan 2005, 13:26
I get D, here is how I did it.

forget about round table just make the sitting that no 2 men are adjacent or women like wise

so the seating looks like this, first chair 4 ways men can sit on it, second chair 4 ways women can sit on it, third chair 3 ways men can sit, fourth chair 3 ways women can sit.

- - - -
M W M W
4 4 3 3 = 144

[/u]
Intern
Joined: 07 Jan 2005
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08 Jan 2005, 07:16
fresinha12 wrote:
I get D, here is how I did it.

forget about round table just make the sitting that no 2 men are adjacent or women like wise

so the seating looks like this, first chair 4 ways men can sit on it, second chair 4 ways women can sit on it, third chair 3 ways men can sit, fourth chair 3 ways women can sit.

- - - -
M W M W
4 4 3 3 = 144

[/u]

Can you explain you reasoning a little bit more. I am confused because there are 8 chairs, not 4??

Thanks
Manager
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08 Jan 2005, 09:47

M1 W1 M2 W2 M3 W3 M4 W4

We have 8 persons: 4 men and 4 women

â€¢ M1 has 8 available places, and he can sit anywhere. So, letâ€™s assume that M1 is setting in the first position, so 1
â€¢ M2 has 3 places available, so it is 3
â€¢ M3 has 2 places available so it is 2
â€¢ M4 has only one place available so it is 1

Letâ€™s continue with women:â€¢ The number of places available for W1, W2, W3 and W4 is 4! than 4P4= 4! /(4-4)!

Final answer is multiplying all the different answers which are 1*3*2*1*4! = 144
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