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mathmath333
 one year ago
counting question
mathmath333
 one year ago
counting question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0In how many can \(4\) men and \(4\) women be seated around round table so that no \(2\) men are in adjacent positions.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0Let's say we had 8 seats A through H dw:1440732939919:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0we can pull out the chairs and form a straight line dw:1440733031604:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0You can have it where the men go in seats A,C,E,G the women go in seats B,D,F,H

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0u mean 4!*4! ways ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0the answer given is 4!*3! ways

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not to butt in, but here is another step

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0go ahead, I'm missing something

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the 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 \(2\times 4!\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but if the answer is really \(4!3!\) i am missing something

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0jim's thomson's answer is with respect to straight line, which can double count some positions on round table (circle)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0I guess it has something to do with this http://mathworld.wolfram.com/CircularPermutation.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oooh i see a ROUND table

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes it is linked with circular permutation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the number of ways to seat 4 people in a round table is not 4! is it 3!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because the table is round, we lose one place in the permutations

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0as stated in circular permutation formula it should be \((41)!\times (41)!\)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440733439379:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0needless to say i am making this up as i go along
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