If $^{n} C_{5} =^{n} C_{6}$ then find $^{13} C_{n}$

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Detailed Solution

$^{n} C_{r} =^{n} C_{s} \Rightarrow r = s or r + s = n^{n} C_{5} =^{n} C_{6} \Rightarrow n = 6 + 5 = 11 \Rightarrow^{13} C_{n} =^{13} C_{11} =^{13} C_{2} \Rightarrow^{13} C_{n} = \frac{13 \times 12}{1 \times 2} = 78$

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