Find n if ^n C_8= ^n C_ 12 - Vidyadip

Question

Find $n$ if ${ }^n C_8={ }^n C_{12}$

✓

Answer

$
{ }^n \mathrm{C}_8={ }^n \mathrm{C}_{12}
$
If ${ }^n C_x={ }^n C_y$, then either $x=y$ or $x=n-y$
$
\therefore 8=12 \text { or } 8=\mathrm{n}-12
$
But $8=12$ is not possible
$
\begin{aligned}
& \therefore 8=\mathrm{n}-12 \\
& \therefore \mathrm{n}=20
\end{aligned}
$

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