Prove that: \[ r \cdot{ }^{n} \mathrm{C}_{r}=n \cdot{ }^{n-1} \mathrm{C}_{r-1} \]

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Prove that:
\[
r \cdot{ }^{n} \mathrm{C}_{r}=n \cdot{ }^{n-1} \mathrm{C}_{r-1}
\]
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