If $^{n} C_{10} =^{n} C_{12}$ , then find n?

120

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22

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12

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2

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Solution

The correct option is A $22$
$^{n} C_{10} =^{n} C_{12}$
We know
$^{n} C_{r} =^{n} C_{n - r}$
$\Rightarrow r + (n - r) = n = 10 + 12 = n \Rightarrow n = 22$
There fore the required value of $n = 22$

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