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AMC / AIME · Stars and Bars · Medium

Stars and Bars: How many positive solutions does math have?

Integer solutions to linear equations.

Try the problem

How many **positive** solutions does x1+x2+x3=11x_1+x_2+x_3=11 have?

Hint and answer

Concept to use

Positive via $y_i=x_i-1$.

Hint

(11−13−1)\binom{11-1}{3-1}.

Answer

45

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