Answer
$360$
Work Step by Step
Expand, cancel, and multiply
$\frac{10!}{7!\cdot2!} = \frac{10\cdot9\cdot8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot2\cdot1} = \frac{10\cdot9\cdot8}{2\cdot1} = 10\cdot9\cdot4 = 360$