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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