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Let's say we had 8 seats A through H
|dw:1440732939919:dw|

we can pull out the chairs and form a straight line
|dw:1440733031604:dw|

You can have it where the men go in seats A,C,E,G
the women go in seats B,D,F,H

ok

u mean 4!*4! ways ?

yep

the answer given is 4!*3! ways

not to butt in, but here is another step

go ahead, I'm missing something

but if the answer is really \(4!3!\) i am missing something

I guess it has something to do with this
http://mathworld.wolfram.com/CircularPermutation.html

oooh i see a ROUND table

yes it is linked with circular permutation

the number of ways to seat 4 people in a round table is not 4! is it 3!

because the table is round, we lose one place in the permutations

as stated in circular permutation formula
it should be \((4-1)!\times (4-1)!\)

|dw:1440733439379:dw|

needless to say i am making this up as i go along