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Math Help - person who sit in a circle

  1. #1
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    person who sit in a circle

    there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table?

    (i ) there is no restriction
    my ans is 7!=5040

    (ii) all teachers must sit together
    the ans is 1008. can someone explain part ii please?
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  2. #2
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    Re: person who sit in a circle

    Quote Originally Posted by delso View Post
    there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table?

    (i ) there is no restriction
    my ans is 7!=5040

    (ii) all teachers must sit together
    the ans is 1008. can someone explain part ii please?
    There are 7 ways to sit the group of teachers together. There are 3! ways of grouping the teachers in each case. Then in each case there are then 4! ways of seating the parents.

    $7*3!*4!=1008$
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  3. #3
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    Re: person who sit in a circle

    in round table, any person can be taken the starting point . am i right? why we would have to times 7 in the working? in round table , the working should be (n-1)! am i right?
    Last edited by delso; July 6th 2014 at 11:42 PM.
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  4. #4
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    Re: person who sit in a circle

    Quote Originally Posted by delso View Post
    in round table, any person can be taken the starting point . am i right? why we would have to times 7 in the working? in round table , the working should be (n-1)! am i right?
    The teachers can be seated in

    ABC
    BCD
    CDE
    DEF
    EFG
    FGA
    GAB

    7 ways
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  5. #5
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    Re: person who sit in a circle

    can i say explain in this way? since the chair is labelled from A to G (in circle), so the position of the first object placed is important. if the chairs are not labelled (in a circle), then i can ignore the 7, which means i have 3! x 4!=144
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  6. #6
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    Re: person who sit in a circle

    Quote Originally Posted by delso View Post
    can i say explain in this way? since the chair is labelled from A to G (in circle), so the position of the first object placed is important. if the chairs are not labelled (in a circle), then i can ignore the 7, which means i have 3! x 4!=144
    you can but it's not the problem you were given.

    It clearly states the chairs are labeled.
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  7. #7
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    Re: person who sit in a circle

    why i cant do in this way? i have 3! arrangment for teacher, i can insert the 3 teacher in between the 4 parents. so my working is 3! x 5! =720
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