Need help setting up a math problem
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    Need help setting up a math problem

    I'm looking over a practice test about to go take my test, and there is one question on the practice test that i have no clue how to set up.

    "Each of 2 countries sends 6 delgates to a negotiating conference. A rectangular table is used with 6 chairs on each long side. If each country is assigned a long side of the table (operation 1), how many seating arrangements are possible?"

    I'm pretty sure it has something to do with combinations, but still don't know what to do next. The answer is 1,036,800 too btw.

    Thanks to anyone who understands this!



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    Re: Need help setting up a math problem

    Got it.



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    Re: Need help setting up a math problem

    6! * 6! * 2

    Each country has 6! ways of sitting in 6 seats, so that's 6! * 6! for two countries sitting on specific sides of the table. Since there are additionally two different configurations for which country is on which side (country A side 1 country B side 2, country A side 2 country B side 1) you multiply that by 2.



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    Re: Need help setting up a math problem

    First seat has 12 choices (all others on that side will be from the same country). The other side will be your standard 6!

    12*5*4*3*2*1*6*5*4*3*2*1=1036800

    EDIT: What mred said would be the correct answer. I missed the "assigned" sides keyword.


    Last edited by ISUAgronomist; 12-07-2010 at 02:33 PM.

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    Re: Need help setting up a math problem

    (6*5*4*3*2*1) one side
    *
    (6*5*4*3*2*1) other side
    *
    2 (delegations switch sides of the table)




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    Re: Need help setting up a math problem

    on one side : 6*5*4*3*2*1=720
    on the other side : 6*5*4*3*2*1=720
    both sides combined : 720*720=518,400
    if the countries switched sides : 518,400*2=1,036,800



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    Re: Need help setting up a math problem

    damn...too slow



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    Re: Need help setting up a math problem

    I understand it now. Didn't really want to go into the lab for one quick question!! Thanks a lot for the help guys!



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    Re: Need help setting up a math problem

    This is fun, we should have these types of competitions regularly! CF.com math bowl.




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    Re: Need help setting up a math problem

    what countries are they from?



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    Re: Need help setting up a math problem

    on one side : 6*5*4*3*2*1=720
    on the other side : 6*5*4*3*2*1=720
    both sides combined : 720*720=518,400
    if the countries switched sides : 518,400*2=1,036,800



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    Re: Need help setting up a math problem




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    Re: Need help setting up a math problem

    Is this a dinner party and is anyone left-handed?




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    Re: Need help setting up a math problem

    I came up with exactly half that number then it dawned on me.
    The countries can switch sides and that gives you the answer.



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    Re: Need help setting up a math problem

    That would be one really long game of musical chairs.



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