Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2015, 02:24
GMAT Club Tests

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many different four-letter words can be formed (the words don't

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Current Student
User avatar
Joined: 31 Aug 2007
Posts: 371
Followers: 1

Kudos [?]: 70 [1] , given: 1

How many different four-letter words can be formed (the words don't [#permalink] New post 12 Dec 2007, 11:15
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (03:08) correct 72% (01:49) wrong based on 81 sessions
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

A. 59
B. 11!/(2!*2!*2!)
C. 56
D. 23
E. 11!/(3!*2!*2!*2!)
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Apr 2015, 04:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern
Intern
avatar
Joined: 13 Jun 2007
Posts: 48
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 12 Dec 2007, 12:21
Difficult one

M E D I T R A N
E R A N
E

E _ _ R
M 7
E 8
D 7
I 7
T 7
R 7
A 8
N 8

So 5x7 + 3x8=35+24=59

Cannot figure out anything other than brute force.
Tried 11C2 which made logic to me, but got 11C2=55

Do you have the answer?
Manager
Manager
avatar
Joined: 03 Sep 2006
Posts: 233
Followers: 1

Kudos [?]: 9 [0], given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 12 Dec 2007, 20:19
My way:

Available letters:

M E D I T R A N (8 letters)

E _ _ R

We have 1 combination for E and 1 combination for R, and also we have 8 combinations for the 2nd letter and 7 combinations for the last letter, so:

E 8 7 R = 1 * 8 * 7 * 1 = 56
Manager
Manager
User avatar
Joined: 11 Aug 2007
Posts: 64
Followers: 1

Kudos [?]: 11 [0], given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 01:28
can somebody explain how to solve this one? would appreciate
VP
VP
avatar
Joined: 22 Nov 2007
Posts: 1104
Followers: 8

Kudos [?]: 242 [0], given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 02:41
young_gun wrote:
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

A. 59
B. 11!/2!*2!*2!
C. 56
D. 23
E. 11!/3!*2!*2!*2!



Please, could you explain that to me so that I can easily understand?? I am very bad at perms!
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2348 [0], given: 359

GMAT ToolKit User Premium Member
Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 03:23
Expert's post
marcodonzelli wrote:
Please, could you explain that to me so that I can easily understand?? I am very bad at perms!


we should complete word E _ _ R using set {M-1, E-2 (one E we use as the first letter), D-1, I-1,T-1,R-1 (one R we use as the last letter) ,A-2,N-2}

So, the set consist of 5 single letters and 3 pairs of letters.

1. for second position we have 8 cases (or 5+3)

2. for third position we have either 8 cases (second letter is from a pair) or 7 cases (second letter is single letter).

Therefore,
N=(3*8+5*7)=59
VP
VP
avatar
Joined: 22 Nov 2007
Posts: 1104
Followers: 8

Kudos [?]: 242 [0], given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 04:17
Please, could you explain that to me so that I can easily understand?? I am very bad at perms![/quote]

we should complete word E _ _ R using set {M-1, E-2 (one E we use as the first letter), D-1, I-1,T-1,R-1 (one R we use as the last letter) ,A-2,N-2}

So, the set consist of 5 single letters and 3 pairs of letters.

1. for second position we have 8 cases (or 5+3)

2. for third position we have either 8 cases (second letter is from a pair) or 7 cases (second letter is single letter).

Therefore,
N=(3*8+5*7)=59

I understand point 1 and point 2 as well...but why N=(3*8+5*7)?thanks
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2348 [0], given: 359

GMAT ToolKit User Premium Member
Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 04:37
Expert's post
marcodonzelli wrote:
I understand point 1 and point 2 as well...but why N=(3*8+5*7)?thanks


for letters of E,A,N at second position we have 8 cases for third one. So, 3*8
for letters of M,D,I,T,R at second position we have 7 cases for third one (we cannot use, for example, M twice). So, 5*7
3 KUDOS received
Intern
Intern
avatar
Joined: 07 Nov 2006
Posts: 14
Followers: 0

Kudos [?]: 4 [3] , given: 0

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 13 Dec 2007, 13:32
3
This post received
KUDOS
young_gun wrote:
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

A. 59
B. 11!/2!*2!*2!
C. 56
D. 23
E. 11!/3!*2!*2!*2!


We have 11 letters after E and R occupied their places. But E, A and N show up twice each. So we have 8 distinct letters for 2 places.
For the second place - 8 letters
for the third - 7 letters
Number of variants - 8*7=56, but we have to take into account additional 3 variants with double letters EAAR, ENNR, EEER.
So the ultimate calculation is 56+3=59
Intern
Intern
User avatar
Joined: 17 Jun 2014
Posts: 19
Followers: 0

Kudos [?]: 23 [0], given: 12

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 04 Apr 2015, 16:54
anybody plz explain why position 2nd and 3rd not like this : 11*10 = 110 ways !
many thanks !
Intern
Intern
avatar
Joined: 01 Apr 2015
Posts: 48
Followers: 0

Kudos [?]: 9 [0], given: 98

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 06 Apr 2015, 13:38
Hi Bunuel, could you please explain the solution in your words ?

Thanks.
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29110
Followers: 4726

Kudos [?]: 49770 [3] , given: 7403

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 07 Apr 2015, 04:33
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Swaroopdev wrote:
Hi Bunuel, could you please explain the solution in your words ?

Thanks.


How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

A. 59
B. 11!/(2!*2!*2!)
C. 56
D. 23
E. 11!/(3!*2!*2!*2!)

E - - R

We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.

We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.

2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.

Total = 56 + 3 = 59.

Answer: A.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 338
Followers: 65

Kudos [?]: 474 [0], given: 83

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 08 Apr 2015, 01:50
Expert's post
In the above problem, if the letters of the word MEDITERRANEAN are allowed to be used multiple times irrespective of their count in the parent word (commonly referred as ‘repetition’ in the P&C parlance), the answer would change. Let me explain the solution for such a case.

We need to fill the 2nd and the 3rd place with letters present in the word MEDITERRANEAN. Since, there are 8 different letters (M, E, D, I, T, R, A, N) in the word MEDITERRANEAN, the 2nd place can be filled with 8 possible letters and the 3rd place can also be filled with 8 possible letters (because, in the case we are discussing here, the letters can be used multiple times, even if they are present only once in the word MEDITERRANEAN).

So, we will have a total of 8*8 = 8^2= 64 possible set of words

Similarly, if the above case is extended to the first and the last letter as well (i.e. we don’t have the constraint of having ‘E’ as the first letter and ‘R’ as the last letter), we will have 8^4 possible sets of words which we can form from the word MEDITERRANEAN.

The key here is to be careful on two points:

Whether letters can be used more than their count in the parent word, in this case MEDITERRANEAN.

If yes, then we need to focus only on different letters present in the parent word, in this case the 8 different letters in the parent word MEDITERRANEAN.

Hope it helps!

Regards
Harsh
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Intern
Intern
avatar
Joined: 04 Mar 2015
Posts: 1
Followers: 0

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

Re: How many different four-letter words can be formed (the words don't [#permalink] New post 11 Apr 2015, 03:04
I used a diffrent method:

we can also solve this question with combinatorics fairly easy:

after E and R are set as the first and the last letters we are left with the two middle ones.

since both E and R show up more then once we can still use all the original letters for the two remeaining blanks.

actually our bank of letters will now look as so:
M=1
E=2
D=1
I=1
T=1
R=1
A=2
N=2

if all remaining letters would have shown up just once the answer would have been:
#=8P2=8!/(8-2)!=56

but since we are left with 3 letters that show up more then once (E,A,N) we need to add the possibilty of using the same letter twice, meaning:
#=8P2+3=59

so the answer is A.
Re: How many different four-letter words can be formed (the words don't   [#permalink] 11 Apr 2015, 03:04
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic In how many different ways can the letters of the word usre123 6 23 Sep 2014, 03:41
3 How many 3 letter (not necessarily distinct) words can be formed NickHalden 2 05 Sep 2014, 23:09
7 Experts publish their posts in the topic How many words can be formed using all the letters of "EQUAT cyberjadugar 8 16 Jun 2012, 19:38
14 Experts publish their posts in the topic How many words can be formed by taking 4 letters at a time jatt86 17 14 Apr 2010, 04:33
7 Experts publish their posts in the topic From 7 consonants and 5 vowels, how many words can be formed Itzrevs 19 28 Dec 2005, 18:45
Display posts from previous: Sort by

How many different four-letter words can be formed (the words don't

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.