Answer
$79,833,600$ different exercise routines.
Work Step by Step
1) It is not a sequence of choices.
2) The order in which the exercises are done matters.
3) Only 9 of 12 exercises are selected.
Permutation of 12 distinct exercises taken 9 at a time:
$_{12}P_9=\frac{12!}{(12-9)!}=\frac{12!}{3!}=\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1}=79,833,600$
