Question 1077185
We have 10 slots. In the first slot, there are 10 choices. In the second slot there are 9 choices since the professor can't visit the same place again. The pattern continues until we count down to 1.


Multiply out those values: 10*9*8*7*6*5*4*3*2*1 = <font color=red>3,628,800</font> which is the final answer. 


Side note: this can be shortened using factorial notation. So we can say 10! = 3,628,800. The exclamation mark means "multiply from that integer all the way down to 1".