(b) Given, $\ ^{n}C_{12} = \ ^{n}C_{6}$ or $\ ^{n}C_{n - 12} = \ ^{n}C_{6}$ $\Longrightarrow n - 12 = 6 \Longrightarrow n = 18$ $\therefore\ \ ^{n}C_{2} = \ ^{18}C_{2} = 153$
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.