Q. If $\ ^{n}C_{12} = \ ^{n}C_{6}$, then $\ ^{n}C_{2}$ is equal to

A) 72
B) 153
C) 306
D) 2556
Explanation

(b)
Given, $\ ^{n}C_{12} = \ ^{n}C_{6}$
or $\ ^{n}C_{n - 12} = \ ^{n}C_{6}$
$\Longrightarrow n - 12 = 6 \Longrightarrow n = 18$
$\therefore\ \ ^{n}C_{2} = \ ^{18}C_{2} = 153$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.