Solve the following

Question:

If 35Cn +7 = 35C4n − 2 , then write the values of n.

Solution:

${ }^{35} C_{n+7}={ }^{35} C_{4 n-2}$

$n+7+4 n-2=35 \quad\left[\because^{n} C_{x}=^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$

$\Rightarrow 5 n=30$

$\Rightarrow n=6$

And, $n+7=4 n-2$

$\Rightarrow n=3$

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