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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|
You can have it where the men go in seats A,C,E,G the women go in seats B,D,F,H
u mean 4!*4! ways ?
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 \((4-1)!\times (4-1)!\)
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