## vishal_kothari 3 years ago Seven people are in an elevator which stops at ten floors. In how many ways can they get o the elevator...

1. vishal_kothari

get*off*the

2. nubeer

not sure maybe 10! x 7!

3. vishal_kothari

no..

4. FoolForMath

\( 11^7 \) ?

5. vishal_kothari

no..

6. FoolForMath

7. FoolForMath

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

8. vishal_kothari

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

9. vishal_kothari

10. FoolForMath

answer is \( 10^7 \) then.

11. AnwarA

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

12. vishal_kothari

how?

13. FoolForMath

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

14. FoolForMath

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

15. across

FFM is correct.

16. vishal_kothari

ya..

17. across

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.\[\]

18. FoolForMath

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.

19. FoolForMath

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

20. vishal_kothari

ok..

21. across

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

22. FoolForMath

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

23. FoolForMath

@across: well just increase the numbers :P

24. across

Let's try 7 floors and 10 people.

25. FoolForMath

or more generally any \( r \gt n \)

26. FoolForMath

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

27. across

Whoops.

28. FoolForMath

@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.

29. pokemon23

anyone willing to explain me about square roots?

30. FoolForMath

Anyways, always excuse my solecism :P

31. robtobey

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]