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Q)

If $^nC_{12}=^nC_8,$ then $n = ?$

$\begin{array}{1 1} 6 \\ 12 \\ 20 \\ 30 \end{array}$

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A)
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  • $^nC_r=^nC_{n-r}$
Since $^nC_r=^nC_{n-r}$,
$^C_{12}=^nC_8\:\:\Rightarrow\:12=n-8$
$\Rightarrow\:n=20$
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