If $^{n} C_{8} =^{n} C_{12}$ , find $n$

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Solution

From the standard formula we get:
$^{n} C_{8} =^{n} C_{12}$
$^{n} C_{8} =^{n} C_{n - 12}$ $[∵^{n} C_{r} =^{n} C_{n - r}]$
$⟹ 8 = n - 12$
$∴ n = 12 + 8 = 20$

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