AMC / AIME · Stars and Bars · Medium

Stars and Bars: How many nonnegative solutions to math?

Integer solutions to linear equations.

Try the problem

How many nonnegative solutions to x+y+z=15x+y+z=15?

Hint and answer

Concept to use

Positive via $y_i=x_i-1$.

Hint

(15+3−12)\binom{15+3-1}{2}.

Answer

136

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