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

(a) 20 (b) 12 (c) 6 (d) 30

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Solution

Given that, $^{n} C_{12} =^{n} C_{8}$

$\Rightarrow^{n} C_{n - 12} =^{n} C_{8}$ $[∵^{n} C_{r} =^{n} C_{n - r}]$

$\Rightarrow n - 12 = 8$

$\Rightarrow n = 12 + 8 = 20$

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