SOLUTION: A building has 8 floors. Suppose 7 people got in the elevator on the ground floor and that each person gets off on the upper floors. What is the probability that they got off on di

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Question 1014666: A building has 8 floors. Suppose 7 people got in the elevator on the ground floor and that each person gets off on the upper floors. What is the probability that they got off on different floors?
Answer by mathmate(429) (Show Source):
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Question:
A building has 8 floors. Suppose 7 people got in the elevator on the ground floor and that each person gets off on the upper floors. What is the probability that they got off on different floors?

Solution:
For the 7 persons to get off on different floors, there are 7! ways, namely there are 7 persons left to choose from for the second floor, 6 persons for the third floor, etc.
If there is no constraint whatsoever, then each person has 7 choices of floors for a total of 7^7 arrangements.
So the probability of all 7 persons getting off different floors is
P(different floors)==0.0061 (approx.)