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If \({ }^{20} \mathrm{C}_{\mathrm{r}}={ }^{20} \mathrm{C}_{\mathrm{r}-10}\) then \({ }^{18} \mathrm{C}_{\mathrm{r}}\) is equal to
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816
\({ }^{20} \mathrm{C}_{\mathrm{r}}={ }^{20} \mathrm{C}_{\mathrm{r}-10} \Rightarrow \mathrm{r}+(\mathrm{r}-10)=20 \Rightarrow \mathrm{r}=15\)
\(\therefore \quad{ }^{18} \mathrm{C}_{\mathrm{r}}={ }^{18} \mathrm{C}_{15}={ }^{18} \mathrm{C}_3=\frac{18 \cdot 17 \cdot 16}{1 \cdot 2 \cdot 3}=816\)
\(\therefore \quad{ }^{18} \mathrm{C}_{\mathrm{r}}={ }^{18} \mathrm{C}_{15}={ }^{18} \mathrm{C}_3=\frac{18 \cdot 17 \cdot 16}{1 \cdot 2 \cdot 3}=816\)
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