Question

If ${{}^{n}P}_r=720$ and ${{}^{n}C}_r=120$. Find $r$.

Answer 1

As, ${}^n{P}_r=720$, then,

$\frac{n!}{\left(n-r\right)!}=720$ (1)

And,

${}^n{C}_r=120$

$\frac{n!}{r!\left(n-r\right)!}=120$

From equation (1),

$\frac{1}{r!}\times 720=120$

$r!=6$

$r!=3\times 2\times 1$

$r!=3!$

$r=3$