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  1. #1
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    help with math question - combination

    12 men and 10 women should be seated around a round table.
    How many ways are there to do that …

    a. … if we require each woman to sit between two men?
    b. … if we require all women to sit adjacently (i.e. all women, except for two, sit between two women)?
    c. … if they are 10 married couples (and two single males) and each couple is to be seated adjacently?

    can u explain me please how u got to the answers..... thnx
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  2. #2
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    Quote Originally Posted by tukilala View Post
    12 men and 10 women should be seated around a round table. How many ways are there to do that …
    c. … if they are 10 married couples (and two single males) and each couple is to be seated adjacently?
    There are \left( {N - 1} \right)! ways to arrange N distinct items is a circle.
    Here you have twelve distinct items: ten couples and two singles.
    There are \left( {11} \right)! ways to arrange them so that the husband is on his wife’s right.
    But that last condition may hold. So we add a factor 2^{10} \left( {11} \right)! to account for the ways each couple may choose to be seated.
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  3. #3
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    Hello, tukilala!

    12 men and 10 women should be seated around a round table.
    How many ways are there to do that …

    a) if we require each woman to sit between two men?

    Seat the 12 men around the table.
    . . There are 11! possible seatings.

    Place a chair between each of the men.
    Assign the ten women to ten of the twelve empty chairs:
    .There are P(12,10) \,=\,\frac{12!}{2!} ways.

    Answer: . \frac{(11!)(12!)}{2!}




    b) if we require all women to sit adjacently?

    Duct-tape the ten women together.
    Then we have 13 "people" to seat around the table.
    . . There are 12! ways.

    But the ten women can be ordered in 10! ways.

    Answer: . (12!)(10!)




    c. if they are 10 married couples and two single males
    and each couple is to be seated adjacently?

    Duct-tape the married couples together.
    Then we have 12 "people" to seat.
    . . There are 11! ways.

    But each couple has two possible orders: husband-wife or wife-husband.
    . . And there are: 2^{10} orderings.

    Answer: . (11!)(2^{10})

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  4. #4
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    i dont understand what have u done in question a
    what is p(12,10) and why its equal to 12!/2! ways
    and why is the ansewer is ((11!)(12!))/2!

    thnx
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