Probability and Stats permutation problem

[billy2908]

Homework Statement

So here's the problem. There is an elevator w/ 5 people equally likely to get off at any of the 7 floor.

What is the probability that no two passengers will get off the same floor.

Homework Equations

The probability of event should be P(E)= number of event outcome/ number of total outcome

The Attempt at a Solution

Total outcome should be 7^5 since
for first floor there can be 1,2,3,4, or 5 people getting off
second floor there can be 1,...,5 people getting off etc.

But I am not sure how to calculate the number of event outcomes.

 

[Dick]

Total outcome is 7^5 because the first person can choose any of the seven floors to get off on, the second person can choose any of the seven floors to get off on, etc. If they all have to choose different floors then once the first person has chosen, how many choices are left for the second person?