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Math Help - Data Management

  1. #1
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    Data Management

    Need help with these questions:

    Ten people are to be seated at rectangular table. Tanya will sit at the head. Henry must not sit beside either wlison or nacny. How many ways can they be seated.

    how many 7 digit even numbers less than 3 000 000 can be formed using all the digits 1, 2, 2, 3, 5,5,6
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  2. #2
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    Smile not quite sure but maybe it will help ;)

    Tanya to be seated at head of table, which means she can sit at either end.. so there are 2 ways to seat her.

    Holding her spot constant, there are 9! ways to seat the rest of the people.

    but Henry can't sit beside Nancy or Wilson, so find out how many ways Henry can be seated with either (a)Nancy or (b)Wilson MINUS the times when they are all seated together(c), then subtract this from the total.

    (a) = 6!
    (b) = 6!
    (c) = 5!

    So I think the answer is 2+(9!-2x6!+5!)
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  3. #3
    MHF Contributor
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    Quote Originally Posted by agentzero2 View Post
    Need help with these questions:

    Ten people are to be seated at rectangular table. Tanya will sit at the head. Henry must not sit beside either wlison or nacny. How many ways can they be seated.

    how many 7 digit even numbers less than 3 000 000 can be formed using all the digits 1, 2, 2, 3, 5,5,6
    1. With Tanya at the head, there are 9! ways to arrange the rest of the people at the table. Number of ways to seat Henry next to Wilson: 2x8! (factor of two depending on the order in which Henry and Wilson sit, and 8! because the two are considered as a unit). The number of ways to seat Henry next to Nancy is the same. The overlap between those two seating arrangements is to have Henry seated next to both Wilson and Nancy, which is 2x7! (all three are considered as a unit, and there are two ways to order them). So the answer is 9! - (2x8! + 2x8! - 2x7!) which is 9! - 4x8! + 2x7!
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