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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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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.

  2. jim_thompson5910
    • one year ago
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    Let's say we had 8 seats A through H |dw:1440732939919:dw|

  3. jim_thompson5910
    • one year ago
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    we can pull out the chairs and form a straight line |dw:1440733031604:dw|

  4. jim_thompson5910
    • one year ago
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    You can have it where the men go in seats A,C,E,G the women go in seats B,D,F,H

  5. mathmath333
    • one year ago
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    ok

  6. mathmath333
    • one year ago
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    u mean 4!*4! ways ?

  7. jim_thompson5910
    • one year ago
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    yep

  8. mathmath333
    • one year ago
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    the answer given is 4!*3! ways

  9. anonymous
    • one year ago
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    not to butt in, but here is another step

  10. jim_thompson5910
    • one year ago
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    go ahead, I'm missing something

  11. anonymous
    • one year ago
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    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 \(2\times 4!\)

  12. anonymous
    • one year ago
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    but if the answer is really \(4!3!\) i am missing something

  13. mathmath333
    • one year ago
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    jim's thomson's answer is with respect to straight line, which can double count some positions on round table (circle)

  14. jim_thompson5910
    • one year ago
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    I guess it has something to do with this http://mathworld.wolfram.com/CircularPermutation.html

  15. anonymous
    • one year ago
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    oooh i see a ROUND table

  16. mathmath333
    • one year ago
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    yes it is linked with circular permutation

  17. anonymous
    • one year ago
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    the number of ways to seat 4 people in a round table is not 4! is it 3!

  18. anonymous
    • one year ago
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    because the table is round, we lose one place in the permutations

  19. mathmath333
    • one year ago
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    as stated in circular permutation formula it should be \((4-1)!\times (4-1)!\)

  20. triciaal
    • one year ago
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    |dw:1440733439379:dw|

  21. anonymous
    • one year ago
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    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

  22. anonymous
    • one year ago
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    needless to say i am making this up as i go along

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