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# M14-25

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 00:53
00:00

Difficulty:

25% (medium)

Question Stats:

71% (00:36) correct 29% (00:51) wrong based on 123 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

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 00:53
1
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.

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Joined: 03 Feb 2015
Posts: 14
GMAT 1: 680 Q47 V36
GMAT 2: 720 Q49 V39

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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.

bunuel,
why are we not dividing it by 2!*2! ( reason- L and E are repeated)
Math Expert
Joined: 02 Sep 2009
Posts: 54376

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25 Mar 2015, 03:50
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.

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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Joined: 15 Mar 2015
Posts: 13
Concentration: Strategy, Finance
GMAT 1: 700 Q47 V39
GMAT 2: 710 Q47 V41
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GPA: 3.3
WE: Information Technology (Real Estate)

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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.

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...
Intern
Joined: 27 Oct 2015
Posts: 19

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12 Dec 2016, 05:20
1
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.

-----

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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Joined: 02 Sep 2009
Posts: 54376

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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.

-----

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
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29 Mar 2017, 23:55
Manager
Joined: 20 Jun 2014
Posts: 51
GMAT 1: 630 Q49 V27
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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.
Re: M14-25   [#permalink] 09 Aug 2017, 23:08
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# M14-25

Moderators: chetan2u, Bunuel

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