Question

If ${}^n{C}_{12}={}^n{C}_6$, then ${}^n{C}_2$ is equal to

• A. 72
• B. 153
• C. 306
• D. 2556

Answer 1

Answer: (B)

Given ${}^n{C}_{12}={}^n{C}_6$
or ${}^n{C}_{n-12}={}^n{C}_6$
$\Rightarrow n-12=6$
$\Rightarrow n=18$
$\therefore n{C}_2={}^{18}{C}_2=\frac{18\times 17}{2\times 1}$
$=153$