Question: If 15C3r = 15Cr + 3 , then r is equal to
(a) 5
(b) 4
(c) 3
(d) 2
Solution:
(c) 3
$3 r+r+3=15 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$
$\Rightarrow 4 r+3=15$
$\Rightarrow 4 r=12$
$\Rightarrow r=3$
