Answer
$_7P_7=5,040$
Work Step by Step
RECALL:
$_nP_r = \dfrac{n!}{(n-r)!}$
Use this definition to have:
$\require{cancel}
_7P_7=\dfrac{7!}{(7-7)!}
\\_7P_7=\dfrac{7!}{0!}
\\_7P_7 = \dfrac{7!}{1}
\\_7P_7 = 7!
\\_7P_7=7(6)(5)(4)(3)(2)(1)
\\_7P_7=5,040$
