AMC / AIME · Stars and Bars · Easy

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

Integer solutions to linear equations.

Try the problem

How many **positive** integer solutions does x1+x2=10x_1+x_2=10 have?

Hint and answer

Concept to use

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

Hint

Stars and bars: (10−12−1)\binom{10-1}{2-1}.

Answer

9

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