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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] New post 28 Feb 2012, 05:14
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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] New post 28 Feb 2012, 05:22
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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.

Answer: B.

Hope it's clear.
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Re: Permutations and Combinations Question!!! [#permalink] New post 28 Feb 2012, 05:31
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.

Answer: B.

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] New post 14 Apr 2012, 19:33
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] New post 14 Apr 2012, 23:24
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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] New post 25 Mar 2013, 05:44
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] New post 03 May 2014, 07:57
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Four persons enter a lift on the ground floor of a nine-floor building [#permalink] New post 23 Mar 2015, 06:14
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 help me in finding solution by P(Event)= 1- P(Non-event)

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] New post 23 Mar 2015, 06:18
Expert's post
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 help me in finding solution by P(Event)= 1- P(Non-event)

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


Merging topics.

Please search before posting. Thank you.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Four persons enter the lift of a seven storey building at [#permalink] New post 23 Mar 2015, 07:35
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] New post 23 Mar 2015, 08:13
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 help me in finding solution by P(Event)= 1- P(Non-event)

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] New post 23 Mar 2015, 11:12
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 help me in finding solution by P(Event)= 1- P(Non-event)

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.

:-D :-D :-D :-D :-D
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Re: Four persons enter the lift of a seven storey building at [#permalink] New post 23 Mar 2015, 21:07
Expert's post
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] New post 23 Mar 2015, 21:35
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.
_________________

Thanks,
Lucky

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Re: Four persons enter the lift of a seven storey building at   [#permalink] 23 Mar 2015, 21:35
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