Answer
$5040$
Work Step by Step
$P(n,r)=\displaystyle \frac{n!}{(n-r)!}$.
Factorials:
$n!=n(n-1)!=n(n-1)(n-2)!=...$
$n!=n(n-1)(n-2)\cdots(3)(2)(1)$
$ 0!=1,\qquad$ by definition.
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$P(10,4)=\displaystyle \frac{10!}{(10-4)!}=\frac{10\times 9\times 8\times 7\times 6!}{6!}$
$=10\times 9\times 8\times 7$ = $5040$