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Math Help - permutation and combination

  1. #1
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    Question permutation and combination

    HOW many solutions are dere to the equation:
    x1+x2+x3+x4+x5=21
    where xi=1,2,3,4,5, is a non-negative integer such that

    c)0<=x1<=10
    d)0<=x1<=3,1<=x2<4,and x3>=15?


    kindly give full soln,not simply ans
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  2. #2
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    Re: permutation and combination

    Quote Originally Posted by panelopy123 View Post
    HOW many solutions are dere to the equation:
    x1+x2+x3+x4+x5=21
    where xi=1,2,3,4,5, is a non-negative integer such that
    c)0<=x1<=10
    d)0<=x1<=3,1<=x2<4,and x3>=15?
    These are done with generating functions.
    d) Expand \left( {\sum\limits_{k = 0}^{10} {x^k } } \right)\left( {\sum\limits_{k = 1}^4 {x^k } } \right)\left( {\sum\limits_{k = 15}^{20} {x^k } } \right)\left( {\sum\limits_{k = 0}^5 {x^k } } \right)^2
    The coefficient of x^{21} answers your question.
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  3. #3
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    Re: permutation and combination

    Attached
    Attached Thumbnails Attached Thumbnails permutation and combination-002.jpg   permutation and combination-001.jpg  
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