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# Four persons enter the lift of a seven storey building at

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Four persons enter the lift of a seven storey building at [#permalink]

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28 Feb 2012, 06:14
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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
[Reveal] Spoiler: OA
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Re: Permutations and Combinations Question!!! [#permalink]

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28 Feb 2012, 06:22
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kiran882 wrote:
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

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.

Hope it's clear.
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Re: Permutations and Combinations Question!!! [#permalink]

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28 Feb 2012, 06:31
Bunuel wrote:
kiran882 wrote:
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

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.

Hope it's clear.

Oh!! Its very easy question!
Thanks for ur lucid explanation!
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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14 Apr 2012, 20:33
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?
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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15 Apr 2012, 00:24
1
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Expert's post
shankar245 wrote:
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?

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.
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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25 Mar 2013, 06:44
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..
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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03 May 2014, 08:57
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Four persons enter a lift on the ground floor of a nine-floor building [#permalink]

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23 Mar 2015, 07:14
Four persons enter a lift on the ground floor of a nine-floor building. Each person is equally likely to leave the lift at any floor except the ground floor. What is the probability of all the persons leaving the lift at different floors?

A. 105/512
B. 105/256
C. 112/243
D. 1560/2147
E. 7/8

I have solved the above; but I have a doubt.-
P(Event) + P (Non-Event) =1
Where event =all leaving at different floors.

Please explain how to calculate using the Non-Event method.
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 07:18
samichange wrote:
Four persons enter a lift on the ground floor of a nine-floor building. Each person is equally likely to leave the lift at any floor except the ground floor. What is the probability of all the persons leaving the lift at different floors?

A. 105/512
B. 105/256
C. 112/243
D. 1560/2147
E. 7/8

I have solved the above; but I have a doubt.-
P(Event) + P (Non-Event) =1
Where event =all leaving at different floors.

Please explain how to calculate using the Non-Event method.

Merging topics.

Please search before posting. Thank you.
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Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 08:35
kiran882 wrote:
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

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.
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 09:13
samichange wrote:
Four persons enter a lift on the ground floor of a nine-floor building. Each person is equally likely to leave the lift at any floor except the ground floor. What is the probability of all the persons leaving the lift at different floors?

A. 105/512
B. 105/256
C. 112/243
D. 1560/2147
E. 7/8

I have solved the above; but I have a doubt.-
P(Event) + P (Non-Event) =1
Where event =all leaving at different floors.

Please explain how to calculate using the Non-Event method.

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
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 12:12
chetan2u wrote:
samichange wrote:
Four persons enter a lift on the ground floor of a nine-floor building. Each person is equally likely to leave the lift at any floor except the ground floor. What is the probability of all the persons leaving the lift at different floors?

A. 105/512
B. 105/256
C. 112/243
D. 1560/2147
E. 7/8

I have solved the above; but I have a doubt.-
P(Event) + P (Non-Event) =1
Where event =all leaving at different floors.

Please explain how to calculate using the Non-Event method.

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

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.

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Re: Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 22:07
Lucky2783 wrote:
kiran882 wrote:
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

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.

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.
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Re: Four persons enter the lift of a seven storey building at [#permalink]

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23 Mar 2015, 22:35
VeritasPrepKarishma wrote:
Lucky2783 wrote:
kiran882 wrote:
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

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.

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.

thank you karishma for the clarifications.
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Thanks,
Lucky

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Re: Four persons enter the lift of a seven storey building at [#permalink]

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04 Aug 2015, 01:23
kiran882 wrote:
Bunuel wrote:
kiran882 wrote:
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

Hi Bunuel, I got the OE however Please let me know where i am wrong in this , No of ways for 1st floor to get persons = 5(0,1,2,3,4)similarly for all other floors , so i got 5^6
Re: Four persons enter the lift of a seven storey building at   [#permalink] 04 Aug 2015, 01:23
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