If $^{n} C_{7} =^{n} C_{4}$ . Find n.

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Solution

$C_{7}^{n} = C_{4}^{n}$
We know that, $C_{r}^{n} = C_{n - r}^{n}$
$\Rightarrow C_{7}^{n} = C_{n - 7}^{n} = C_{4}^{n}$
$\Rightarrow n - 7 = 4$
$∴ n = 11$

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