There are 12 different pizza toppings, and Arturo must rank his top 5 in order. How many different possible rankings are there? Okay, I understand that I need to do 12*11*10*9*8 but I don't understand the next step. Could someone explain what and why?

Question

directrix · Answer

This is Arturo's top 5 in order possibilities:  12*11*10*9*8.

>I don't understand the next step.

So, what is the next step about which you are asking? 

@idiealot

anonymous · Answer

You're right and that was a dumb question. Thank you. I thought I had to divide it by something.

directrix · Answer

No, it is not a dumb question.
I was just second-guessing myself and about to ask if the order mattered which makes this a permutation. Then, I re-read "in order" and decided your work is correct.

Had the question been "In how many ways can Arturo choose his top 5 pizza toppings?" then the problem would have been a combination one and the order would not have mattered.

What makes this sort of problem sometimes confusing is the language, e.g., rank. But, the problem stated "rank in order" and cleared possible confusion.