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Math Help - Help needed on combination problem

  1. #1
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    Help needed on combination problem

    Prove that the total number of selectionsthat can be made out of the letters "DADDY DID A DEADLY DEED" is 1919.

    does anyone have the solution to this??
    -thank you
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  2. #2
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    Re: Help needed on combination problem

    Quote Originally Posted by blackhat98 View Post
    Prove that the total number of selectionsthat can be made out of the letters "DADDY DID A DEADLY DEED" is 1919.
    does anyone have the solution to this??
    Please tell us what is meant by a selection?

    POST SCRIPT:
    I made a guess as to what this question means.
    If one expands \left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)
    we get a polynomial of degree 19.
    Each coefficient in the expansion tell the number of possible selections.
    For example: the term in the expansion 191x^9 tells us that there are 191 ways to select nine items from that list.
    If we sum all the coefficients we get 1920.
    But that includes the empty selection.
    Remove it and there is 1919.
    Last edited by Plato; December 29th 2011 at 04:32 AM.
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  3. #3
    Super Member ILikeSerena's Avatar
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    Re: Help needed on combination problem

    Nice method!
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  4. #4
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    Re: Help needed on combination problem

    Quote Originally Posted by Plato View Post
    Please tell us what is meant by a selection?

    POST SCRIPT:
    I made a guess as to what this question means.
    If one expands \left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)
    we get a polynomial of degree 19.
    Each coefficient in the expansion tell the number of possible selections.
    For example: the term in the expansion 191x^9 tells us that there are 191 ways to select nine items from that list.
    If we sum all the coefficients we get 1920.
    But that includes the empty selection.
    Remove it and there is 1919.
    thank you Plato....
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