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Math Help - How many different

  1. #1
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    How many different

    There are 20 questions in the multichoice-exam and there are 4 answer alternatives on every question.
    Only one alternative is always correct.
    How many different answer papers is possible to form in which there are 70% of the answers correct?
    Here is my solution ( I am not sure is this same formula needed here, but it might be right ) and that 70% would be * 0,7



    (20 + 4 - 1)!
    __________ * 0,7 =
    20! * ( 4 - 1)!
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  2. #2
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    Re: How many different

    Quote Originally Posted by stevetall View Post
    There are 20 questions in the multichoice-exam and there are 4 answer alternatives on every question.
    Only one alternative is always correct.
    How many different answer papers is possible to form in which there are 70% of the answers correct?
    There are \binom{20}{14} ways to have exactly fourteen correct answers.
    There are 3^6 ways to answer the other six incorrectly.
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  3. #3
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    Re: How many different

    Thank you.
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  4. #4
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    Re: How many different

    I just want to make sure that I understood.

    So this is 20 over 14

    20
    14

    and should there be 4 *, I mean;

    20 * 4
    14

    Because each question contains 4 alternatives. This probably is a big number.
    It cannot be * 4! , but it might be * 4
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  5. #5
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    Re: How many different

    Quote Originally Posted by stevetall View Post
    So this is 20 over 14
    \binom{20}{14}=\frac{20!}{14!\cdot 6!}=38760
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  6. #6
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    Re: How many different

    Ah, of course...

    Now it is clear.

    Thanks!
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