Elevator problem

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Raed93

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An elevator carries 100 passengers. If it operatein a building of 25 floors and stop literally at each floor to drop passengers. What is the total number of ways that the elevator would load the passengers ?
 
Raed93 said:
An elevator carries 100 passengers. If it operatein a building of 25 floors and stop literally at each floor to drop passengers. What is the total number of ways that the elevator would load the passengers ?
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Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.
 
Raed93 said:
An elevator carries 100 passengers. If it operatein a building of 25 floors and stop literally at each floor to drop passengers. What is the total number of ways that the elevator would load the passengers ?
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There is no answer possible unless you are given more information about what the loading objective or what the method of unloading is. Have you given the exact wording as you have it?
 
I have a number of questions regarding this problem.

Are there 25 floors or 26 floors (lobby to 25 other floors)?

Are all 100 people getting on at the same time?

You ask What is the total number of ways that the elevator would load the passengers? Are you sure you want to say load instead of unload?

You can simply post the problem exactly as written.
 
Raed93 said:
An elevator carries 100 passengers. If it operates in a building of 25 floors and stop literally at each floor to drop passengers. What is the total number of ways that the elevator would load the passengers ?/QUOTE]
I think that Jomo is correct that you mean unload. This is a pure occupancy problem: how many can \(100\) people get off the elevator onto \(25\) floors. This is the same as asking "how many ways can \(N\) identical objects be placed into \(K\) distinct cells.
The answer is worth learning: \(\dbinom{N+K-1}{N}=\dfrac{(N+K-1)!}{N!(K-1)!}\) In your question \(K=25~\&~N=100\)
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pka, I still have my main concern. If everyone gets on at a certain floor then why would anyone get off that floor? Or am I thinking to hard?
 
Jomo said:
pka, I still have my main concern. If everyone gets on at a certain floor then why would anyone get off that floor? Or am I thinking to hard?
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I think that you are over-thinking what the question is really about. I really think that this question is written by someone trying to be clever in asking students to apply the identical balls into distinct cells problem.
 
I am not sure that otis is allowed to service elevator problems in general.
 
pka said:
… question [was] written by someone trying to be clever in asking students to apply the identical balls into distinct cells problem.
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That occurred to me; however, my next thought was, "but they botched it". People are not identical objects.

?
 
Jomo said:
It's just that if 100 people get on the elevator I am not clear why someone would get off that same floor?
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Form a scenario that makes sense, then. Put 100 people in the elevator, and then send the elevator to 25 other floors, with people leaving at each of those floors (without anyone getting on).

Jomo said:
… Are all 100 people getting on at the same time? …
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The exercise statement begins by telling us the elevator "carries 100 people". It doesn't matter how, when or where they all got on. At some point, 100 people are on the elevator, and the elevator then travels to 25 different floors.

Are you sure you want to say load instead of unload?
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At first, I thought that was a typo. Later, I realized that an elevator can distribute or "load" people onto floors. That work for you?

What I don't like is the assumption that all the people are identical clones with the same name.

By the way, did you try to visualize an elevator that holds 100 people?

?
 
Otis said:
What I don't like is the assumption that all the people are identical clones with the same name.
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I don't think that that you can really mean that. Suppose you were asked about the number of ways to place one hundred red balls into twenty five different cells each of which can hold all the balls. If we were to add to the description that the balls are numbered 0 to 99, then would that change the count? If it would change it, please explain how. To think is matters is a category error; we care not who gets off but just how many get off on any floor.
 

pka said:
There is no answer possible unless you are given more information about what the loading objective or what the method of unloading is. Have you given the exact wording as you have it?
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first of all thank you, it just load off the passengers there is no way to load .
 
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