If $^{n} C_{4} =^{n} C_{7}$ find the $n$ .

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Solution

Given,
$^{n} C_{4} =^{n} C_{7} \Rightarrow^{n} C_{r} =^{n} C_{n - r} \Rightarrow r + (n - r) = n \Rightarrow 4 + 7 = n \Rightarrow n = 11$
Hence the correct answer is $11$

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