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Math Help - Finding total number of combinations which include some specific numbers

  1. #1
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    Finding total number of combinations which include some specific numbers

    My math is not good and I am not sure in which forum section I should post my question.



    Let's say I want to group numbers between 1 and 50 with 4 columns:
    1 2 3 4
    1 2 3 5
    1 2 3 6
    ...
    2 3 4 5
    2 3 4 6
    ...
    47 48 49 50


    To find the total possible combinations,we do:
    50*49*48*47
    __________
    1*2*3*4
    This formula gives the maximum possible combinations.

    My question is,what would the formula be to find maximum of how many combinations of
    these numbers include number 1 and 2(for example)?
    Last edited by Awareness; April 26th 2013 at 03:35 PM.
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  2. #2
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    Re: Finding total number of combinations which include some specific numbers

    Hey Awareness.

    You would need to just restrict the state space to those which have a 1 and 2.

    Hint: Take a look at this formula:

    Inclusion?exclusion principle - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Finding total number of combinations which include some specific numbers

    Quote Originally Posted by Awareness View Post
    My math is not good and I am not sure in which forum section I should post my question.
    Let's say I want to group numbers between 1 and 50 with 4 columns:
    1 2 3 4
    1 2 3 5
    1 2 3 6...
    2 3 4 5
    2 3 4 6
    ...
    47 48 49 50


    To find the total possible combinations,we do:
    50*49*48*47
    __________
    1*2*3*4
    This formula gives the maximum possible combinations.
    My question is,what would the formula be to find maximum of how many combinations of
    these numbers include number 1 and 2(for example)?
    There are so many difficulties with this qauestion that there no good place to start.
    FIRST: neither 1 nor 50 is between 1 and 50.
    If you want include them then say numbers from 1 to 50.

    With that linguistic understanding then your numbers look like \boxed{~A~}\boxed{~B~}\boxed{~C~}\boxed{~D~}

    There are 50 choices for A, 49 choices for B, 48 choices for C, and 47 choices for D.
    Last edited by Plato; April 26th 2013 at 08:19 PM.
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