Four persons enter the lift of a seven storey building at

Question

Four persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor

A. 720
B. 1296
C. 1540
D. 1478
E. 360

Bunuel · Accepted Answer

Welcome to GMAT Club. Below is a solution to your question.

Each person out of 4 has 6 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 6*6*6*6=6^4. Now, there is no need to actually calculate this value: 6^4 will have 6 as the units digit and there is only one option (B) which offers such a number.

Answer: B.

Hope it's clear.

shankar245 · Answer

Hi Buneul,

When they say 4 and 6 floors should we not account the possibility that

1st floor : A

2 nd floor B

3rd floor C
4th floor D

alos combinations like

1st floor AB

or BC

Am i confused?

Bunuel · Answer

Try to consider simpler example (3 floors, 2 persons) and see whether the cases when both of them get out on the same floor are counted in 3^2. You'll see that they are:

I -- II -- III  (Floors)
A -- B
B -- A
A -- * -- B
B -- * -- A
* -- A -- B
* -- B -- A
AB
* -- AB
* -- * -- AB

Hope it helps.

bluecatie1 · Answer

Hi Brunel,

I tried a different approach which I thought would also be applicable in this situation but got a different answer. Can you please tell me where did I go wrong? Here we go:

Option 1: All 4 people get out on one of the six floors. This can be done in 6 ways (2nd floor, 3rd floor, 4th floor, etc)

Option 2: 3 people get out together on one floor, and I person on a different floor. This can be done in the following manner:
 
 4C3 * 1C1 * 6!/4! = 120 ways

Option 3: 2 people get out on one floor and 2 on another floor: 
 
 4C2 * 2C2 * 6!/4! = 180 ways

Option 4: 2 people get out on one floor and then 1 and 1. Again we have

4C2 * 6!/3! = 720 ways

Option 5: One person on each floor:

6!/2! = 360 ways

A total of 1386 ways. But my answers is different than yours..

Lucky2783 · Answer

Just want to check one doubt regarding ground floor, does it represents floor# 0 OR Floor# 1 ? 
The country where i live ground floor represents 0 , and with that in mind 
i was trying 7*7*7*7 , none of the option has 1 as unit digit so i inferred that ground floor here represents floor #1 . 
are we expected to have such knowledge specific to a country ?
for eg: 1 have one permutation/combination question 
QU: A family of 5 is going for a summer vacation and they decided to drive the car (with 5 seats ) to a hill station . 
family is composed of 2 daughters ,1 son and parents. only parents can drive . none of the girl want to sit adjacent to a right side window of the car. 
how many possible combinations are there ? 
considering in USA the steering is on left side while in ASIA the steering in on right side , we will have two different answers for this question.

chetan2u · Answer

hi,
why do you want it to become complicated by solving this by non-event.
rather if it asks you for probability of people not leaving on different floors, you would use non event method..
choose this method when it simplifies calculations- example.. atleast one thing is done.. etc

samusa · Answer

Hi Thanks. I just solved it little while ago by the non-event method and arrived at the correct answer. I found it little complicated to solve by the non-event method. Took me 30 minutes to solve by the non-event method. :-D

KarishmaB · Answer

A seven storey building means a building with seven floors - it doesn't matter how you name them. You could call them "floor 1 to floor 7" or "ground floor to floor 6". If the seven storey building has a ground floor (as given in the question), it will have 6 more floors above it. So either ways, your answer will be the same irrespective of the country to which you belong. 
As for the car question, you will not see such a discrepancy in an actual GMAT question.

kkrrsshh · Answer

Hi  Bunuel ,

Can you please tell me why can't we take it this way:4 can be out on 1st flr, 4 can be out on 2nd flr.. so effectively it will 4^6?

vs224 · Answer

Each person has 6 floor option to choose from:
1: 6 option
2: 6 option etc
..
4 person so 6^4

Kinshook · Answer

Given: Four persons enter the lift of a seven storey building at the ground floor.

Asked: In how many ways can they get out of lift on any floor other than ground floor?

# of ways can they get out of lift on any floor other than ground floor  = (7-1)^4 = 6^4 = 1296

IMO B

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Four persons enter the lift of a seven storey building at

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