I'm working on this problem:
An elevator in a building starts with 5 passengers and stops at seven 7 floors. If each passenger is equally likely to get an any floor and all the passengers leave independently of each other, what is the probability that no two passengers will get off at the same floor?
I figure you could do 7 P 5 - since the first guy has 7 floors he can get off on, the second 6, etc. But do I need to account for the order that the people can choose their floor, and therefore multiply that by 5 factorial? Or am I approaching this incorrectly in the first place?