Question

If ${}^n{C}_8={}^n{C}_2,$ find ${}^n{C}_2.$

Answer 1

Here ${}^n{C}_8{=}^n{C}_2\Rightarrow {}^n{C}_8{=}^n{C}_{n-2}$

$[\because {}^n{C}_r{=}^n{C}_{n-r}]$

$\Rightarrow 8=n-2[\because {}^n{C}_x{=}^n{C}_y\Rightarrow x=y]$

$\Rightarrow n=10$

$\therefore {}^n{C}_2{=}^{10}{C}_2=\frac{10!}{2!8!}=45.$