If $^{n} C_{12} =^{n} C_{5}$ , find the value of $n$ .

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Solution

$n_{C_{12}} = n_{C_{5}} n = ?$

$\frac{n!}{(n - 12)! 12!} = \frac{n!}{(n - 5)! 5!}$

$n - 5 = 12$ $n - 12 = 5$

$n = 17$ $n = 17$

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