Answer
$_{11}P_9=19,958,400$
Work Step by Step
Using $
_nP_r=\dfrac{n!}{(n-r)!}
$ or the Permutation of $n$ taken $r,$ the given expression, $
_{11}P_9
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{11!}{(11-9)!}
\\\\&=
\dfrac{11!}{2!}
\\\\&=
\dfrac{11(10(9)(8)(7)(6)(5)(4)(3)(2!)}{2!}
\\\\&=
\dfrac{11(10(9)(8)(7)(6)(5)(4)(3)(\cancel{2!})}{\cancel{2!}}
\\\\&=
11(10(9)(8)(7)(6)(5)(4)(3)
\\&=
19,958,400
.\end{align*}
Hence, $
_{11}P_9=19,958,400
.$
