How many letter combinations can be composed of letters of : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 Feb 2017, 15:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many letter combinations can be composed of letters of

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 05 Oct 2008
Posts: 274
Followers: 3

Kudos [?]: 400 [0], given: 22

How many letter combinations can be composed of letters of [#permalink]

### Show Tags

06 Nov 2008, 10:11
00:00

Difficulty:

(N/A)

Question Stats:

56% (01:33) correct 44% (00:29) wrong based on 21 sessions

### HideShow timer Statistics

How many letter combinations can be composed of letters of the word LEVEL if all these combinations have to begin with L and end with E?

* 4
* 6
* 10
* 12
* 24
Senior Manager
Joined: 04 Aug 2008
Posts: 377
Followers: 5

Kudos [?]: 34 [0], given: 1

Re: Combinations [#permalink]

### Show Tags

06 Nov 2008, 10:44
so u r changing three places within the LEVEL

1x2x3=6

B
_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Senior Manager
Joined: 05 Oct 2008
Posts: 274
Followers: 3

Kudos [?]: 400 [0], given: 22

Re: Combinations [#permalink]

### Show Tags

07 Nov 2008, 05:53
How many letter combinations can be composed of letters of the word LEVEL if all these combinations have to begin with L and end with E?

Not really
LEVEL
L - L1
E - E1
V - V
E - E2
L - L2

Since the Es and Ls could be either of the two, we have four options -
Ist-----------Last
L -----------E
L1 -----------E1
L -----------E
L1 -----------E1

The center 3 have - 6 - combinations

Hence the total ways the letters can be arranged is 24
VP
Joined: 05 Jul 2008
Posts: 1430
Followers: 39

Kudos [?]: 363 [0], given: 1

Re: Combinations [#permalink]

### Show Tags

07 Nov 2008, 06:27
How do you differentiate between the same letter L? I thought about the number of ways of picking one L and one E out of 2 L's and 2 E's respectively.

Write down and see if you really get 24. In the end L1=L2 & E1=E2 and your combinations will reduce down to 6
Senior Manager
Joined: 05 Oct 2008
Posts: 274
Followers: 3

Kudos [?]: 400 [0], given: 22

Re: Combinations [#permalink]

### Show Tags

08 Nov 2008, 03:45
Ah! you are right icandy - thanks.
kudos given
Senior Manager
Joined: 18 Aug 2009
Posts: 435
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 8

Kudos [?]: 121 [0], given: 16

Re: Combinations [#permalink]

### Show Tags

22 May 2010, 21:53
Can somebody elaborate on this problem,
I can not get which method you guys are using to come to the solution.

Slot method or using specific combinatorics formula?

My thinking was that Letter L could be chosen in two ways, Letter E in 2 ways as well, and the middle V only one way, thus
I am getting 4
I know it is not correct answer.
Thank you.
_________________

Never give up,,,

Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7243

Kudos [?]: 96333 [0], given: 10737

Re: Combinations [#permalink]

### Show Tags

23 May 2010, 02:09
mirzohidjon wrote:
Can somebody elaborate on this problem,
I can not get which method you guys are using to come to the solution.

Slot method or using specific combinatorics formula?

My thinking was that Letter L could be chosen in two ways, Letter E in 2 ways as well, and the middle V only one way, thus
I am getting 4
I know it is not correct answer.
Thank you.

How many letter combinations can be composed of letters of the word LEVEL if all these combinations have to begin with L and end with E?

Keep it simple:

$$L---E$$: three distinct letters are left - V, E and L. We can place them in three slots in 3!=6 # of ways (basically it's the same as # of permutations of 3 distinct letters - 3!).
_________________
Senior Manager
Joined: 18 Aug 2009
Posts: 435
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 8

Kudos [?]: 121 [0], given: 16

Re: Combinations [#permalink]

### Show Tags

23 May 2010, 10:23
Thank you,
Now I got it!
_________________

Never give up,,,

Senior Manager
Joined: 05 Oct 2008
Posts: 274
Followers: 3

Kudos [?]: 400 [0], given: 22

Re: Combinations [#permalink]

### Show Tags

01 Jun 2010, 06:36
Check he differnce between the two questions

How many letter combinations can be composed of letters of the word LEVEL if all these combinations have to begin with L and end with E?

* 4
* 6
* 10
* 12
* 24

How many ways can the letter - TRUST - be arranged?

* 30
* 60
* 6
* 3
* 24

Ans to both is B
Intern
Joined: 24 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 13

Re: Combinations [#permalink]

### Show Tags

24 Apr 2011, 08:02
Hi Bunuel,
Isn't the question ambiguous? At its current form, why should we not include word combinations which would have just one or two letters in between L and E. For example, should not LVE or LLVE be included? Dont see anything in the question which would stop us from including such combinations. Am I wrong? Please help. Thanks.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 423

Kudos [?]: 1530 [0], given: 4

Re: Combinations [#permalink]

### Show Tags

24 Apr 2011, 10:09
neel1982 wrote:
Hi Bunuel,
Isn't the question ambiguous? At its current form, why should we not include word combinations which would have just one or two letters in between L and E. For example, should not LVE or LLVE be included? Dont see anything in the question which would stop us from including such combinations. Am I wrong? Please help. Thanks.

As I read the question, you're perfectly right - there's no reason from the wording to assume we need to use all 5 of the letters (though if you don't need to use all five letters, the right answer is not among the choices).

Perhaps worse still, the question asks how many 'combinations' we can make. In mathematics, a 'combination' is a selection *where order does not matter*. If we are creating 'words', obviously order does matter. It's crucially important that the question be clear about whether order matters here, and it isn't. The language of the question is horrible; the original post is so old I doubt we'll ever know the source, but whatever it is, I wouldn't recommend using it.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 119 [0], given: 42

Re: Combinations [#permalink]

### Show Tags

24 Apr 2011, 17:42
Ian ,

dont we have to consider chosing one L out of two and one E out of two for the edges? how come answer is its just 6! then?

Please clarify.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 423

Kudos [?]: 1530 [0], given: 4

Re: Combinations [#permalink]

### Show Tags

24 Apr 2011, 19:27
Spidy001 wrote:
Ian ,

dont we have to consider chosing one L out of two and one E out of two for the edges? how come answer is its just 6! then?

Please clarify.

I'm afraid I don't understand your question - what do you mean by 'edges'?
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 119 [1] , given: 42

Re: Combinations [#permalink]

### Show Tags

24 Apr 2011, 20:41
1
This post received
KUDOS
i meant start and end.

we have 2 L's and 2 E's right? Let me know if this approach is right?

selecting one L out 2 * 3 distinct letter permutations * selecting one E out of 2

= 2c1 * 3! * 2c1

finally we divide this by 2! *2! for because we have 2 L's and 2 E's

= 2c1 * 3! * 2c1 / (2! *2!) = 6
Re: Combinations   [#permalink] 24 Apr 2011, 20:41
Similar topics Replies Last post
Similar
Topics:
11 How many different 4 letter combinations can be created from the lette 7 09 Aug 2015, 11:00
5 How many 5 letter combinations can be made from the letters 3 18 Jul 2014, 10:53
40 In how many ways can 3 letters out of 5 distinct letters A 22 18 Nov 2011, 00:39
2 How many eight letter words exist that are composed of Xs an 6 19 May 2011, 06:15
64 How many combinations of three letters taken from letters 22 02 Dec 2007, 13:29
Display posts from previous: Sort by

# How many letter combinations can be composed of letters of

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.