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Thread: Counting number of solutions for an inequality

  1. March 12th 2009, 09:57 PM #1
    qtpipi
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    Counting number of solutions for an inequality


    I'm stuck. Please help. Thanks.
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  2. March 13th 2009, 02:55 AM #2
    Plato
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    \sum\limits_{j = 0}^n {{j+k-1}\choose j}
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  3. March 13th 2009, 04:28 PM #3
    awkward
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    Quote Originally Posted by qtpipi View Post

    I'm stuck. Please help. Thanks.
    Hint:

    Notice that if x_1 + \dots + x_k \leq n
    where 0 \leq x_i for all i, then

    x_1 + \dots +x_k + x_{k+1} = n
    where 0 \leq x_i for all i.
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« antisymmetric | Moved, New question »

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