Question

If ${}^n{P}_r=1680$ and ${}^n{C}_r=70$. find $r$.

Answer 1

$\frac{1680}{r!}=70$

$\Rightarrow 1680=70(r!)$

$\Rightarrow r!=\frac{1680}{70}=24$

$\Rightarrow r!=2\times 2\times 3\times 4=4!$

$\therefore r=4$