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9 students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?

Please explain, not just answer!

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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")

Answer: 362880
User PeanutsMonkey
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