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Math Help - Accumulating Numbers

  1. #1
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    Solving for a given combination

    I am way stumped. I know how to find combinations, but I have no clue how to find them with the combination given.

    To furnish a room, a decorator is to select 2 chairs and 2 tables from a collection in a warehouse that are all different from each other. If there are 5 chairs in the warehouse, and 150 different combinations are possible. How many tables are in the warehouse?

    The correct answer is 6, but I can't figure out how to get there. I can't even seem to plug in the correct answer to my calculations to reach the number 150.
    Last edited by KingNathan; June 23rd 2011 at 01:15 PM.
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  2. #2
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    Re: Accumulating Numbers

    Quote Originally Posted by KingNathan View Post
    To furnish a room, a decorator is to select 2 chairs and 2 tables from a collection in a warehouse that are all different from each other. If there are 5 chairs in the warehouse, and 150 different combinations are possible. How many tables are in the warehouse?
    \binom{5}{2}\binom{n}{2}=\frac{5!}{2!\cdot3!}\cdot  \frac{n!}{2(n-2)!}=5(n)(n-1)=150

    Can you solve that?
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  3. #3
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    Re: Accumulating Numbers

    Quote Originally Posted by Plato View Post
    \binom{5}{2}\binom{n}{2}=\frac{5!}{2!\cdot3!}\cdot  \frac{n!}{2(n-2)!}=5(n)(n-1)=150

    Can you solve that?
    No sir.

    I now understand the values to the left of the first equal sign. The rest looks like japanese to me. I understand both of the numerators, but I can't understand why the first fraction's denominator is 2! * 3!, nor why there is (n-2) in the second fraction's denominator.
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  4. #4
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    Re: Accumulating Numbers

    Quote Originally Posted by KingNathan View Post
    No sir.
    I now understand the values to the left of the first equal sign. The rest looks like japanese to me. I understand both of the numerators, but I can't understand why the first fraction's denominator is 2! * 3!, nor why there is (n-2) in the second fraction's denominator.
    You do realize that there is no way for you to do these if you don't know the basics.
    Where is your textbook? Where are your lecture notes?
    Find them. Then look up how one evaluates \binom{n}{k}.
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  5. #5
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    Re: Accumulating Numbers

    Quote Originally Posted by Plato View Post
    You do realize that there is no way for you to do these if you don't know the basics.
    Where is your textbook? Where are your lecture notes?
    Find them. Then look up how one evaluates \binom{n}{k}.
    I am not taking a course, nor am I receiving a grade for any question I post on the forum. I am studying for the GMAT to receive admission to get my MBA. Please rest assured that before I posted this question, I spent a considerable amount of time researching through test prep books and the internet. I am a tactile learner, and quite frankly, the more difficult problems are worth more than the easy ones, which leads me to ask for help from the kind people on this forum. Knowing how to solve this particular problem will do absolutely nothing for me, however, learning what the terms stand for in the equation does help me immensely.
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  6. #6
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    Re: Accumulating Numbers

    Quote Originally Posted by KingNathan View Post
    I am studying for the GMAT to receive admission to get my MBA. [F]rankly, the more difficult problems are worth more than the easy ones, which leads me to ask for help from the kind people on this forum. Knowing how to solve this particular problem will do absolutely nothing for me, however, learning what the terms stand for in the equation does help me immensely.
    In a past life, I severed as an ‘outside member’ of an admissions committee for an MBA program. I can assure you that some programs are very mathematically orientated. The GMAT is designed to tell admissions committees how well prepared a candidate is. So if I were you. I would rethink your statement in red.
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  7. #7
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    Re: Accumulating Numbers

    Quote Originally Posted by Plato View Post
    In a past life, I severed as an ‘outside member’ of an admissions committee for an MBA program. I can assure you that some programs are very mathematically orientated. The GMAT is designed to tell admissions committees how well prepared a candidate is. So if I were you. I would rethink your statement in red.
    I am well aware of what my MBA program coursework will entail. I already score above the 70th percentile of the GMAT on practice tests, well above the requirements for my admission. I am taking the initiative to try and further my score, which leads me to ask for help on a small percentage of the problems that I cannot figure out by myself or with the study materials given to me. Without a proper understanding of each portion of a problem, I cannot ensure success in answering them the way they are formatted on the test, nor in a data sufficiency format.

    So unfortunately, I do not have a textbook, lecture notes, or an instructor to consult, which leads me here to the Math Help Forum. For help with math. And if consulting you kind people here helps me significantly in my endeavor, I also intend to donate heavily in appreciation. Are you still willing to answer my questions on this particular problem so I can increase my understanding? Because the tone I received from you makes me feel unwelcome to ask for more help.
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