Here's the question you clicked on:
vishal_kothari
Seven people are in an elevator which stops at ten floors. In how many ways can they get o the elevator...
what is the answer ?
@across: I don't think that's the right answer.
(a) 7^10 (b) 10^7
answer lies between this two...
answer is \( 10^7 \) then.
Oh, I think the answer that across gave assumed that each one gets off in a different floor?
The problem is modeled as " how many ways can n distinct object can be divided in r distinct groups " some groups may be empty.
My earlier answer assumes the super-set and I over counted few other cases.
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.\[\]
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.
@across: wanna try a variation " atleast one should get off in each floor" ? ; )
In this case, though, there are more floors than there are people. :p
@vishal kothari: It's a bit hard, don't attempt it if you don't need it.
@across: well just increase the numbers :P
Let's try 7 floors and 10 people.
or more generally any \( r \gt n \)
Sorry it should be: or more generally any \( r<n \) pertaining to my above model.
@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.
anyone willing to explain me about square roots?
Anyways, always excuse my solecism :P
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]