9students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?explain, not just answer!

We have 9 slots. For slot one, we have 9 choices to pick from in order to fill that appointment. After a student is selected, they can't be selected again. The second slot will have 8 choices. The same will apply to the third but now there are 7 choices. This pattern continues until we count down to 1

Multiply out 9, 8, 7, ..., 3, 2, 1 to get

9*8*7*6*5*4*3*2*1 = 362,880
(note: this concept shows up a lot in probability and counting problems, so much so that it's given a special name of "factorial")

362880