counting question

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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In how many can \(4\) men and \(4\) women be seated around round table so that no \(2\) men are in adjacent positions.
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|

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Other answers:

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
the way you did it you assigned a man to sit in seat A, but it could be woman so if i am not mistaken it is \(2\times 4!\)
but if the answer is really \(4!3!\) i am missing something
jim's thomson's answer is with respect to straight line, which can double count some positions on round table (circle)
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|
i think maybe they reason like this seating four men in a round table is 3! ways, but now we have lost the circularity (if that is a word) and have four spaces in which to put the 4 women, so 4! ways there
needless to say i am making this up as i go along

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