I need help proving that $(m-1)^{n-1}*n^{m-2}=\binom{n+m-1}{n}$.
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The statement is false. Let $m=2$ and $n=2$. Then $$(2-1)^{2-1}\cdot2^{2-2}=1\neq3={2+2-1\choose2}$$
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