Solve the following
Question:

If 18Cx = 18Cx + 2, find x.

Solution:

Given:

${ }^{18} C_{X}={ }^{18} C_{X}+2$

By using ${ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x=y$ or $n=x+y$ we get,

$18=x+x+2$

$\Rightarrow 2 x=16$

$\Rightarrow x=8$