Answer
$504$
Work Step by Step
This is the same as asking for the number of permutations of $9$ people taken $3$ at a time. $_nP_r=\frac{n!}{(n-r)!}$, hence here: $_9P_3=\frac{9!}{(9-3)!}=\frac{9!}{6!}=9\cdot8\cdot7=504$
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