Question

If ${}^n{P}_r$ $=$ 5040, then $(n,r)$ $=$

• A. (9,4)
• B. (10,4)
• C. (11,3)
• D. (11,4)

Answer 1

Answer: (B)

(10,4)

${}^n{P}_r$ $=\frac{n!}{(n-r)!}$.
Now $5040$ $=10\left(9\right)\left(8\right)\left(7\right)$
$=\frac{10!}{\left(6\right)!}$
$=\frac{10!}{(10-4)!}$
$={}^{10}{P}_4$
Hence, $n=10$ and $r=4$