Question

If ${}^n{C}_{15}{=}^n{C}_8$, then the value of ${}^n{C}_{21}$ is

• A. $254$
• B. $250$
• C. $253$
• D. None of these

Answer 1

The correct option is C $253$

Given, ${}^n{C}_{15}={}^n{C}_8$
$\Rightarrow {}^n{C}_{n-15}={}^n{C}_8$
$\therefore n-15=8\Rightarrow n=23$
Now, ${}^n{C}_{21}={}^{23}{C}_{21}$
$=\frac{\left(23\right)!}{2!\times \left(21\right)!}$
$=\frac{23\times 22}{2}=23\times 11=253$.