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M14-25

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M14-25 [#permalink]

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New post 16 Sep 2014, 00:53
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Question Stats:

73% (00:35) correct 27% (00:49) wrong based on 107 sessions

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In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4
B. 6
C. 10
D. 12
E. 24
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:53
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Official Solution:

In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4
B. 6
C. 10
D. 12
E. 24

We need all possible arrangements which fit the following form: \(L---E\). Three distinct letters left (\(V\), \(E\) and \(L\)) can be arranged in three slots between \(L\) and \(E\) in \(3!=6\) ways.

Answer: B
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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: M14-25 [#permalink]

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New post 25 Mar 2015, 03:45
Bunuel wrote:
Official Solution:

In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4
B. 6
C. 10
D. 12
E. 24

We need all possible arrangements which fit the following form: \(L---E\). Three distinct letters left (\(V\), \(E\) and \(L\)) can be arranged in three slots between \(L\) and \(E\) in \(3!=6\) ways.

Answer: B



bunuel,
why are we not dividing it by 2!*2! ( reason- L and E are repeated)

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New post 25 Mar 2015, 03:50
Expert's post
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harDill wrote:
Bunuel wrote:
Official Solution:

In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4
B. 6
C. 10
D. 12
E. 24

We need all possible arrangements which fit the following form: \(L---E\). Three distinct letters left (\(V\), \(E\) and \(L\)) can be arranged in three slots between \(L\) and \(E\) in \(3!=6\) ways.

Answer: B



bunuel,
why are we not dividing it by 2!*2! ( reason- L and E are repeated)


Because we are told that the first letter (L) and the last letter (E) are fixed. Only the three letters (V, E and L) between them can be arranged.
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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.


What are GMAT Club Tests?
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Re: M14-25 [#permalink]

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New post 14 Sep 2015, 18:33
Bunuel wrote:
harDill wrote:
Bunuel wrote:
Official Solution:

In how many ways can the letters of the word LEVEL be arranged so that the first letter is \(L\) and the last letter is \(E\)?

A. 4
B. 6
C. 10
D. 12
E. 24

We need all possible arrangements which fit the following form: \(L---E\). Three distinct letters left (\(V\), \(E\) and \(L\)) can be arranged in three slots between \(L\) and \(E\) in \(3!=6\) ways.

Answer: B



bunuel,
why are we not dividing it by 2!*2! ( reason- L and E are repeated)


Because we are told that the first letter (L) and the last letter (E) are fixed. Only the three letters (V, E and L) between them can be arranged.


How do we know not to count the arrangements of the alternate L and alternate E in the end spots? Is there verbiage that would have indicated otherwise if they did not count as the same? i.e.

Arrangement 1
L1,E1,V,L2,E2

Arrangement 2
L2,E1,V,L1,E2

etc...

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New post 12 Dec 2016, 05:20
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How do we know not to count the arrangements of the alternate L and alternate E in the end spots? Is there verbiage that would have indicated otherwise if they did not count as the same? i.e.

My answer:

-----

First position: Choosing 1 L out of 2 L = 2 ways

Second, Third and Fourth : 3 Letters in 3! ways = 6

Last Position: 1 E out of 2 E's = 2 ways

Therefore, Total no of ways : 2*6*2 = 24.

Hence E

Kindly assist.

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New post 12 Dec 2016, 07:14
dsheth7 wrote:
How do we know not to count the arrangements of the alternate L and alternate E in the end spots? Is there verbiage that would have indicated otherwise if they did not count as the same? i.e.

My answer:

-----

First position: Choosing 1 L out of 2 L = 2 ways

Second, Third and Fourth : 3 Letters in 3! ways = 6

Last Position: 1 E out of 2 E's = 2 ways

Therefore, Total no of ways : 2*6*2 = 24.

Hence E

Kindly assist.


I think the best way to understand why this is wrong to list all possible cases. You'll see that there are only 6 cases, not 24:
LEVLE
LELVE
LVELE
LVLEE
LLEVE
LLVEE
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132742 [0], given: 12360

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New post 29 Mar 2017, 23:55
please refer to mississippi rule, you can find answers to your questions

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Re: M14-25 [#permalink]

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New post 09 Aug 2017, 23:08
dsheth7

you will have to divide this number by 2!*2! as L and E are repeats
24/4 = 6.

Kudos [?]: 14 [0], given: 24

Re: M14-25   [#permalink] 09 Aug 2017, 23:08
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