Last visit was: 19 Nov 2025, 10:59 It is currently 19 Nov 2025, 10:59
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
samcot
avatar
Joined: 11 Sep 2011
Last visit: 11 Oct 2012
Posts: 6
Own Kudos:
14
 [13]
Posts: 6
Kudos: 14
 [13]
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 10:08
2
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

75% (01:00) correct 25% (04:31) wrong based on 32 sessions

History

Date
Time
Result
Not Attempted Yet
How many words of 4 letters can be formed from the word "MEDITERRANEAN"?
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
76,997
 [8]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,997
 [8]
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 21:41
2
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!
Show more

You cannot use a single step permutation here. You will need to first select and then arrange since selection will vary in each case.

We have 8 distinct letters: M, E, D, I, T, R, A, N

Then there are some repetitions: 3E, 2R, 2A, 2N

In how many ways can you make a 4 letter word?

Case 1: All different letters
From the 8 distinct letters, you choose 4 and arrange them.
= 8C4 * 4!

Case 2: 2 letters same, others different
For the 2 same letters, choose one from the 4 which are repeated in 4C1 ways. Then to choose 2 other letters, pick two from the rest 7 distinct letters in 7C2 ways. Then arrange them in 4!/2! ways (you divide by 2! because one letter is repeated)
= 4C1 * 7C2 * 4!/2!

Case 3: 2 letters same, 2 letters same
Choose 2 letters from the 4 which are repeated in 4C2 ways. Then arrange them in 4!/(2!*2!) ways (2 letters are repeated so you divide by 2! twice)
= 4C2 * 4!/(2!*2!)

Case 4: 3 letters same, fourth different
Only 'E' appears 3 times so E must be chosen. You can choose the fourth letter from the other 7 letters in 7C1 ways. Arrange them in 4!/3! ways
= 7C1 * 4!/3!

All four letters cannot be the same since no letter appears four times.

To get the final answer, we will need to add the result from all the cases. I wouldn't worry about doing it. This isn't a GMAT type question. Needs a long monotonous approach. GMAT questions can be solved quickly and usually have a trick. This question is useful only to help you understand the basics of permutation and combination.
General Discussion
User avatar
Capricorn369
User avatar
Joined: 11 May 2011
Last visit: 06 May 2019
Posts: 233
Own Kudos:
225
Given Kudos: 84
Schools: Wharton Exec '21 (WL) Berkeley EMBA"20 (A)
GMAT 1: 680 Q49 V30
Posts: 233
Kudos: 225
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!
Show more

Total number of letters = 13, Repetations - 3E, 2R, 2N, 2A
Answer - 13C4/(3!*2!*2!*2!)

Cheers!
avatar
samcot
avatar
Joined: 11 Sep 2011
Last visit: 11 Oct 2012
Posts: 6
Own Kudos:
14
Posts: 6
Kudos: 14
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 10:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ajay369
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!

Total number of letters = 13, Repetations - 3E, 2R, 2N, 2A
Answer - 13C4/(3!*2!*2!*2!)

Cheers!
Show more

13C4/(3!*2!*2!*2!)= 14.895... can the no of words be negative??
This approach is wrong i think since it is not a combination problem..

the approach to the solution should be sth like this :

no of words without repetition = 8*7*6*5 =1680
+
no of words with repetition=????


or

no of words without considering the repetition= 13P4
-
no of words that are repeated


thanks in advance!!!
User avatar
Capricorn369
User avatar
Joined: 11 May 2011
Last visit: 06 May 2019
Posts: 233
Own Kudos:
225
Given Kudos: 84
Schools: Wharton Exec '21 (WL) Berkeley EMBA"20 (A)
GMAT 1: 680 Q49 V30
Posts: 233
Kudos: 225
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 11:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@samcot - Yes...I know its incorrect. Typed during my meeting without thinking much :oops:
Will respond again :-D

Sorry for inconvenience.
Cheers!
User avatar
naveen1003
User avatar
Joined: 09 Jun 2011
Last visit: 06 Oct 2011
Posts: 13
Own Kudos:
3
 [1]
Posts: 13
Kudos: 3
 [1]
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 11:49
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!
Show more
13 letters, 3e,2r,2a,2n,m,d,i,t..
if all 4 different: 8C4*4!
if 2 different and one repeat (abca) -> 4C1*7C2* (4!/2!)
if 2 same and other 2 same (aabb) -> 4C2* (4!/2!)
if 3 same, 1 different:(aaab) 1C1*7C1*(4!/3!)
if all four same: 0
add all....
User avatar
Capricorn369
User avatar
Joined: 11 May 2011
Last visit: 06 May 2019
Posts: 233
Own Kudos:
225
Given Kudos: 84
Schools: Wharton Exec '21 (WL) Berkeley EMBA"20 (A)
GMAT 1: 680 Q49 V30
Posts: 233
Kudos: 225
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 12:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
naveen1003
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!
13 letters, 3e,2r,2a,2n,m,d,i,t..
if all 4 different: 8C4*4!
if 2 different and one repeat (abca) -> 4C1*7C2* (4!/2!)
if 2 same and other 2 same (aabb) -> 4C2* (4!/2![highlight]*2![/highlight])
if 3 same, 1 different:(aaab) 1C1*7C1*(4!/3!)
if all four same: 0
add all....
Show more


Looks correct! only one above correction.
avatar
samcot
avatar
Joined: 11 Sep 2011
Last visit: 11 Oct 2012
Posts: 6
Own Kudos:
14
Posts: 6
Kudos: 14
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 20:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
naveen1003
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!
13 letters, 3e,2r,2a,2n,m,d,i,t..
if all 4 different: 8C4*4!
if 2 different and one repeat (abca) -> 4C1*7C2* (4!/2!)
if 2 same and other 2 same (aabb) -> 4C2* (4!/2!)
if 3 same, 1 different:(aaab) 1C1*7C1*(4!/3!)
if all four same: 0
add all....
Show more

I always try to solve this kind of problem with permutation...

if all 4 different: 8C4*4!
this I understood ,as 8C4*4!= 8P4

where as i am not being able to interpret the followings: when repetition is there
if 2 different and one repeat (abca) -> 4C1*7C2* (4!/2!)

if 2 same and other 2 same (aabb) -> 4C2* (4!/2!)

It would be of great help if you can elucidate on the cases of repetition.

Thanks in advance!!!
avatar
samcot
avatar
Joined: 11 Sep 2011
Last visit: 11 Oct 2012
Posts: 6
Own Kudos:
14
Posts: 6
Kudos: 14
How many words of 4 letters can be formed from the word "MED 13 Sep 2011, 22:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
samcot
Please guide me to how to get the answer for the below question..

How many words of 4 letters can be formed from the word "MEDITERRANEAN"?

thanks in advance!!!

You cannot use a single step permutation here. You will need to first select and then arrange since selection will vary in each case.

We have 8 distinct letters: M, E, D, I, T, R, A, N

Then there are some repetitions: 3E, 2R, 2A, 2N

In how many ways can you make a 4 letter word?

Case 1: All different letters
From the 8 distinct letters, you choose 4 and arrange them.
= 8C4 * 4!

Case 2: 2 letters same, others different
For the 2 same letters, choose one from the 4 which are repeated in 4C1 ways. Then to choose 2 other letters, pick two from the rest 7 distinct letters in 7C2 ways. Then arrange them in 4!/2! ways (you divide by 2! because one letter is repeated)
= 4C1 * 7C2 * 4!/2!

Case 3: 2 letters same, 2 letters same
Choose 2 letters from the 4 which are repeated in 4C2 ways. Then arrange them in 4!/(2!*2!) ways (2 letters are repeated so you divide by 2! twice)
= 4C2 * 4!/(2!*2!)

Case 4: 3 letters same, fourth different
Only 'E' appears 3 times so E must be chosen. You can choose the fourth letter from the other 7 letters in 7C1 ways. Arrange them in 4!/3! ways
= 7C1 * 4!/3!

All four letters cannot be the same since no letter appears four times.

To get the final answer, we will need to add the result from all the cases. I wouldn't worry about doing it. This isn't a GMAT type question. Needs a long monotonous approach. GMAT questions can be solved quickly and usually have a trick. This question is useful only to help you understand the basics of permutation and combination.
Show more


Case 2: 2 letters same, others different
For the 2 same letters, choose one from the 4 which are repeated in 4C1 ways. Then to choose 2 other letters, pick two from the rest 7 distinct letters in 7C2 ways. Then arrange them in 4!/2! ways (you divide by 2! because one letter is repeated)
= 4C1 * 7C2 * 4!/2!

Why it is not 4C1*1! * 7C2*2! *4!/2!
Since 7C2 can be arranged themselves in 2! ways ..rt?

Let me know what i am missing

Thanks!!!
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
76,997
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,997
How many words of 4 letters can be formed from the word "MED 14 Sep 2011, 22:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
samcot

Case 2: 2 letters same, others different
For the 2 same letters, choose one from the 4 which are repeated in 4C1 ways. Then to choose 2 other letters, pick two from the rest 7 distinct letters in 7C2 ways. Then arrange them in 4!/2! ways (you divide by 2! because one letter is repeated)
= 4C1 * 7C2 * 4!/2!

Why it is not 4C1*1! * 7C2*2! *4!/2!
Since 7C2 can be arranged themselves in 2! ways ..rt?

Let me know what i am missing

Thanks!!!
Show more

Think of it this way:
You have lots of letters. You need to make a four letter word. How will you do it?
You will select 4 letters and then arrange the 4 of them in different ways to get different words.
How do you select the four letters? You say 4C1 (to get the one which is repeated) * 7C2 (any two of the remaining 7)
Your selection is done. You have 4 letters. Now you want to arrange them.
That is done in 4!/2! ways. This includes arranging the 2 distinct letters and the two same ones together.
You don't need to arrange the distinct letters separately. This number includes combinations such as EEMD and EEDM.
User avatar
nishtil
User avatar
Joined: 10 Jan 2011
Last visit: 08 Feb 2015
Posts: 70
Own Kudos:
361
Given Kudos: 25
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE:Consulting (Consulting)
Products:
My Reviews
Posts: 70
Kudos: 361
How many words of 4 letters can be formed from the word "MED 30 Sep 2011, 03:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I don't think this type of question will appear on GMAT.... any very good qestion to understand the difference between permutation and combination
User avatar
foookato
User avatar
Joined: 16 Nov 2024
Last visit: 22 Jun 2025
Posts: 14
Own Kudos:
11
Given Kudos: 33
Location: United States
Posts: 14
Kudos: 11
How many words of 4 letters can be formed from the word "MED 10 Feb 2025, 08:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
for the ones that calculated, its 24,948,000 aka 13!/(2!)(2!)(2!)(3!)
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts