There are 12 different pizza toppings, and arturo must rank his top 6 in order. how many different possible rankings are there?

The first ranking can take 12  ways.
The second ranking can take 12 - 1 = 11 ways
The third ranking can take 12 - 2 = 10 ways
and so until the six rankings are performed.
The product of the six rankings is
12*11*10*9*8*7 = 665,280.

This result is given by the permutations of 6 objects out of 12. It is given by

which yields the same result.

665,280