# Solve the following

Question:

If 15C3r = 15Cr + 3, find r.

Solution:

Given;

${ }^{15} C_{3 r}={ }^{15} C_{r+3}$

$15=3 r+r+3 . \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x=y\right.$ or, $\left.n=x+y\right]$

$\Rightarrow 15=4 r+3$

$\Rightarrow 4 r=12$

$\Rightarrow r=3$