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AMC / AIME · Stars and Bars · Easy

Stars and Bars: How many nonnegative solutions to math?

Integer solutions to linear equations.

Try the problem

How many **nonnegative** solutions to x1+x2+x3+x4=6x_1+x_2+x_3+x_4=6?

Hint and answer

Concept to use

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

Hint

(6+4−14−1)\binom{6+4-1}{4-1}.

Answer

84

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