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  4. If nC12 = nC8, then n is equal to

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Q. If $^{n}C_{12} = \,{}^{n}C_{8}$, then $n$ is equal to

Permutations and Combinations

Solution:

Given, $^{n}C_{12} =\,{}^{n}C_{8} $
$ \therefore \,\,{}^{n}C_{n-2} =\,{}^{n}C_{8} \quad\left(\because \,{}^{n}C_{r} =\,{}^{n}C_{n-r}\right)$
$\Rightarrow n-12 =8$
$ \Rightarrow n = 20$