Question

If ${}^{20}{P}_r=13{\times }^{20}{P}_{r-1}$, then the value of r is________.

Answer 1

$\begin{array}{c}{}^{20}{p}_r=\left(13\right){}^{20}{p}_r-1\end{array}$

$\frac{20!}{(20-r)!}=\frac{13\times 20!}{(20-r+1)!}⟹21-r=13⟹r=8$