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Thread: 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 $\displaystyle \left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)$
    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 $\displaystyle 191x^9$ tells us that there are 191 ways to select nine items from that list.
    If we sum all the coefficients we get $\displaystyle 1920$.
    But that includes the empty selection.
    Remove it and there is $\displaystyle 1919.$
    Last edited by Plato; Dec 29th 2011 at 03:32 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 $\displaystyle \left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)$
    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 $\displaystyle 191x^9$ tells us that there are 191 ways to select nine items from that list.
    If we sum all the coefficients we get $\displaystyle 1920$.
    But that includes the empty selection.
    Remove it and there is $\displaystyle 1919.$
    thank you Plato....
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