Determining the probability from a given situation.

An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.

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Solution Preview 0, at most 4 passengers to get off. It includes the following cases.
1. 4 passengers get off at one floor. We have 8 possibilities.
2. 3 passengers get off at one floor, 1 passenger gets off at another floor. This is a permutation of 2 positions out of 8 positions. ...