Seven people are in an elevator which stops at ten
floors. In how many ways
can they get o the elevator...

Question

Seven people are in an elevator which stops at ten 
floors. In how many ways
can they get o the elevator...

vishal_kothari · Answer

get*off*the

nubeer · Answer

not sure maybe 10! x 7!

vishal_kothari · Answer

no..

anonymous · Answer

$ 11^7 $ ?

vishal_kothari · Answer

no..

anonymous · Answer

what is the answer ?

anonymous · Answer

@across:  I don't think that's the right answer.

vishal_kothari · Answer

(a) 7^10
(b) 10^7

vishal_kothari · Answer

answer lies between this two...

anonymous · Answer

answer is $ 10^7 $ then.

anonymous · Answer

Oh,  I think the answer that across gave assumed that each one gets off in a different floor?

vishal_kothari · Answer

how?

anonymous · Answer

The problem is modeled as " how many ways can n distinct object can be divided in r distinct groups " some groups may be empty.

anonymous · Answer

My earlier answer assumes the super-set and I over counted few other cases.

across · Answer

FFM is correct.

vishal_kothari · Answer

ya..

across · Answer

Think of it in smaller terms: suppose there are three floors and two people; they can get off the elevator in 9 different ways, which is $3^2$ as FFM's model states.

anonymous · Answer

Precisely, my earlier answer assumes that the seven people need not to get off the elevator at all and only some of them get down and all of the other obvious cases.

anonymous · Answer

@across: wanna try a variation " atleast one should get off in each floor" ? ; )

vishal_kothari · Answer

ok..

across · Answer

In this case, though, there are more floors than there are people. :p

anonymous · Answer

@vishal kothari: It's a bit hard, don't attempt it  if you don't need it.

anonymous · Answer

@across: well just increase the numbers :P

across · Answer

Let's try 7 floors and 10 people.

anonymous · Answer

or more generally any $ r \gt n $

anonymous · Answer

Sorry it should be:

or more generally any $ r<n $

pertaining to my above model.

across · Answer

Whoops.

anonymous · Answer

@across: Sorry, that doesn't seem correct, as $ n^{ \underline{r} } $ is not the correct assumption, generally people attempt it with mutual inclusion-exclusion, but there is a even clever way, If you want I can give you a hint but it would be probably a spoiler.

pokemon23 · Answer

anyone willing to explain me about square roots?

anonymous · Answer

Anyways, always excuse my solecism :P

anonymous · Answer

Assume that the elevator riders are considered indistinguishable, for example, 7 warm bodies. There are 11440 ways for them to get off of an elevator servicing 10 floors. http://2000clicks.com/mathhelp/CountingObjectsInBoxes.aspx Refer to: Indistinguishable Objects to Distinguishable Boxes The number of different ways to distribute n indistinguishable balls into k distinguishable boxes is C(n+k-1,k-1). For those who have access to Mathematica the following is a user defined function called Elevator where r is the number of riders and f is the number of floors. Elevator[ r_ , f_ ] := Binomial[ r + f - 1, f - 1]