Question

If ${}^n{C}_9={}^n{C}_8$ find ${}^n{C}_{17}$

Answer 1

Given that,

${}^n{C}_9{=}^n{C}_8$

We know that ${}^n{C}_r{=}^n{C}_{n-r}$

So, here by comparing with given information, we get

$\Rightarrow r=9andn-r=8$

$\Rightarrow n-9=8$

$\Rightarrow n=8+9$

$\Rightarrow n=17$

$\Rightarrow {}^n{C}_{17}={}^{17}{C}_{17}$

Therefore, $\Rightarrow {}^n{C}_{17}=1$