An elevator in kiely hall starts with 6 people and stops in

An elevator in kiely hall starts with 6 people and stops in 9 floors. If every person is equally likely to get off each floor and all people have independently of each other. What is the probability that no 2 passengers will get off at same floor?

Solution

There are 9^6 ways to choose floors.

There are 9P6 ways so that no two people choose the same floor.

Thus,

P(no two are the same) = 9P6 / 9^9 = 0.11380379 [answer]