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    OlympiadMediumCombinatorics7–9

    Stars and Bars

    Estrelas e Barras

    How many non-negative integer solutions does x_{1} + x_{2} + x_{3} = 10 have?

    Use the stars and bars formula: \binom{n+k-1}{k-1}.

    Solution

    Step 1 of 3

    1. 1.Using stars and bars with n=10 and k=3: