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Math Help - Combinations seating order restrictions

  1. #1
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    Combinations seating order restrictions

    Group of 10 men and 10 women.
    Only 8 seats available

    How many arrangements if at least one woman should sit?

    Mary and Gail should both sit, but not beside each other?
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  2. #2
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    Group of 10 men and 10 women.
    Only 8 seats available
    How many arrangements if at least one woman should sit?
    There are C(20,8) total possible arrangements. The best way to find at least 1 woman sitting is to find the number with no woman sitting and subtract from the total. With no woman sitting is C(10,8), only the men.


    Mary and Gail should both sit, but not beside each other?
    Tie Mary and Gail together and pretend they are one big person. Count the number of arrangements that way and subtract from the total number of ways.
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