Answer
$_{11}P_9=19,958,400$
Work Step by Step
Using $
_nP_r=\dfrac{n!}{(n-r)!}
$ or the Permutation of $n$ taken $r,$ then
\begin{align*}\require{cancel}
_{11}P_9&=
\dfrac{11!}{(11-9)!}
\\\\&=
\dfrac{11!}{2!}
\\\\&=
\dfrac{11(10)(9)(8)(7)(6)(5)(5)(4)(3)(2!)}{2!}
\\\\&=
\dfrac{11(10)(9)(8)(7)(6)(5)(5)(4)(3)(\cancel{2!})}{\cancel{2!}}
\\\\&=
11(10)(9)(8)(7)(6)(5)(5)(4)(3)
\\&=
19958400
\end{align*}
Hence $
_{11}P_9=19,958,400
.$
