mathmath333
  • mathmath333
counting question
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
In how many can \(4\) men and \(4\) women be seated around round table so that no \(2\) men are in adjacent positions.
jim_thompson5910
  • jim_thompson5910
Let's say we had 8 seats A through H |dw:1440732939919:dw|
jim_thompson5910
  • jim_thompson5910
we can pull out the chairs and form a straight line |dw:1440733031604:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

jim_thompson5910
  • jim_thompson5910
You can have it where the men go in seats A,C,E,G the women go in seats B,D,F,H
mathmath333
  • mathmath333
ok
mathmath333
  • mathmath333
u mean 4!*4! ways ?
jim_thompson5910
  • jim_thompson5910
yep
mathmath333
  • mathmath333
the answer given is 4!*3! ways
anonymous
  • anonymous
not to butt in, but here is another step
jim_thompson5910
  • jim_thompson5910
go ahead, I'm missing something
anonymous
  • anonymous
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 \(2\times 4!\)
anonymous
  • anonymous
but if the answer is really \(4!3!\) i am missing something
mathmath333
  • mathmath333
jim's thomson's answer is with respect to straight line, which can double count some positions on round table (circle)
jim_thompson5910
  • jim_thompson5910
I guess it has something to do with this http://mathworld.wolfram.com/CircularPermutation.html
anonymous
  • anonymous
oooh i see a ROUND table
mathmath333
  • mathmath333
yes it is linked with circular permutation
anonymous
  • anonymous
the number of ways to seat 4 people in a round table is not 4! is it 3!
anonymous
  • anonymous
because the table is round, we lose one place in the permutations
mathmath333
  • mathmath333
as stated in circular permutation formula it should be \((4-1)!\times (4-1)!\)
triciaal
  • triciaal
|dw:1440733439379:dw|
anonymous
  • anonymous
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
anonymous
  • anonymous
needless to say i am making this up as i go along

Looking for something else?

Not the answer you are looking for? Search for more explanations.