AMC / AIME · Stars and Bars · Easy

Stars and Bars: How many positive solutions to math?

Integer solutions to linear equations.

Try the problem

How many **positive** solutions to x1+x2+x3=9x_1+x_2+x_3=9?

Hint and answer

Concept to use

Nonnegative: $\binom{n+k-1}{k-1}$.

Hint

(9−13−1)\binom{9-1}{3-1}.

Answer

28

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