Five people are on an elevator that can stop at five floors. In how many differe
ID: 3298536 • Letter: F
Question
Five people are on an elevator that can stop at five floors.
In how many different ways can they leave the elevator if they all get off at different floors? (Answer: 14400)
The answers have already been provided. Your goal is to explain as clearly and logically as possible how to arrive at those answers. You can assume that the person reading your solution is familar with all of the techniques and methods discussed in class or in the text, but that they aren’t sure how to arrive at the solution.
Explanation / Answer
(The question seems to be incomplete or incorrect. The actual answer is 120. However, the following answer actually arrives at the intended value with a modification)
The number of people on the elevator = 5
Number of floors = 5
The first person can leave the elevator on any of the 5 floors.
The second person can leave the elevator on one of the 4 remaining floors as the first person already got off a floor.
The third person can leave the elevator on one of the 3 remaining floors.
The fourth person can leave the elevator on one of the 2 remaining floors.
The fifth person has no choice left but to get off on the remaining floor.
Therefore, total number of different ways for the 5 people to leave the elevator
= 5*4*3*2*1
= 120
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The answer below is for taking the elevator again which is likely the missing part of the question
Now if they take the same elevator again, they will leave the elevator in 120 ways
=> Total number of ways to leave the elevator = 120*120 = 14400
(Same answer is encoutered if the question mentions the following:
The five men get into the elevator at five different floors)
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