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Math Help - Counting number of solutions for an inequality

  1. #1
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    Counting number of solutions for an inequality


    I'm stuck. Please help. Thanks.
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  2. #2
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    \sum\limits_{j = 0}^n {{j+k-1}\choose j}
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  3. #3
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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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