An elevator starts with five passengers and stops on eight f

An elevator starts with five passengers and stops on eight floors. If each passenger is equally likely

to get off on any floor, what is the probability that no two passengers will get off on the same floor?

Solution

Note that

P(no two passengers are same) = P(all are unique)

There are 8P5 = 6720 ways for them to get off at distinct floors.

Also, there are 8^5 = 32768 ways for them to get off.

Thus,

P(all unique) = 6720/32768

= 0.205078125 [ANSWER]