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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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A
B
C
D
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Difficulty:

  45% (medium)

Question Stats:

66% (02:16) correct 34% (01:30) wrong based on 74 sessions
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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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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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Re: Four persons enter the lift of a seven storey building at   [#permalink] 03 May 2014, 07:57
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