Question:
If 20Cr = 20Cr−10, then 18Cr is equal to
(a) 4896
(b) 816
(c) 1632
(d) nont of these
Solution:
(b) 816
$r+r-10=20 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$
$\Rightarrow 2 r-10=20$
$\Rightarrow 2 r=30$
$\Rightarrow r=15$
Now, ${ }^{18} C_{r}={ }^{18} C_{15}$
$\therefore{ }^{18} C_{15}={ }^{18} C_{3}$
$\therefore{ }^{18} C_{3}=\frac{18}{3} \times \frac{17}{2} \times 16=816$