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Math Help - permutation with restrictions

  1. #1
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    permutation with restrictions

    There are 10 people to be seated in a row.
    Person A and Person B must be seated next to each other.
    Person C and Person D must NOT be seated next to each other.

    How many arrangements are possible?
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  2. #2
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    Quote Originally Posted by stumped765 View Post
    There are 10 people to be seated in a row.
    Person A and Person B must be seated next to each other.
    Person C and Person D must NOT be seated next to each other.

    How many arrangements are possible?
    We can deal with the first restriction by considering A and B as a single person, but with two different versions (AB and BA), thus with just that restriction it would be 2 * 9!.

    For the second restriction you can think similarly and start with all permutations, then subtract out those that have C and D next to each other. Can you complete it?
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