Question

If ${}^{10}{P}_r=5040$, then find the value of $r$.

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

Given, ${}^{10}{P}_r=5040$
$\Rightarrow \frac{10!}{(10-r)!}=5040$

$\Rightarrow (10-r)!=\frac{9!}{504}=\frac{9\times 8\times 7\times 6!}{504}=6!$

$\therefore r=4$