It is currently 29 Jun 2017, 02:58

### 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

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 different arrangements of letters are possible if

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
How many different arrangements of letters are possible if [#permalink]

### Show Tags

27 Nov 2010, 07:49
5
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (02:07) correct 41% (01:13) wrong based on 294 sessions

### HideShow timer Statistics

How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Math Expert
Joined: 02 Sep 2009
Posts: 39755
How many different arrangements of letters are possible if [#permalink]

### Show Tags

27 Nov 2010, 07:57
2
KUDOS
Expert's post
5
This post was
BOOKMARKED
rxs0005 wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

Since A and E must be among 3 letters then the third letter must be out of B, C and D. 3C1 = 3 ways to choose which one it'll be. Now, 3 different letters (A, E and the third one) can be arranged in 3!=6 ways, so the final answer is 3*6=18.

_________________
Retired Moderator
Joined: 03 Aug 2010
Posts: 240

### Show Tags

03 Dec 2010, 04:01
Bunuel wrote:
rxs0005 wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

I could understand the first part that 3C1 , why cant we have 5C2*3C1

I sometimes fail to understand the basic diff when to apply permutation and when combination ?

if you can give a brief difference... thanks in advance
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Math Expert
Joined: 02 Sep 2009
Posts: 39755

### Show Tags

03 Dec 2010, 05:10
1
KUDOS
Expert's post
hirendhanak wrote:
Bunuel wrote:
rxs0005 wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

I could understand the first part that 3C1 , why cant we have 5C2*3C1

I sometimes fail to understand the basic diff when to apply permutation and when combination ?

if you can give a brief difference... thanks in advance

We are asked about the # of arrangements of 3 letters: {ABE} is a different arrangement from {EBA}, so for every group of 3 letters (for every selection of 3 letters) there will be 3 different arrangements possible and as there are total of 3 groups (3 selections) possible then there will be total of 3*6=18 arrangements.

Generally:
The words "Permutation" and "Arrangement" are synonymous and can be used interchangeably.
The words "Combination" and "Selection" are synonymous and can be used interchangeably.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39755
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

01 Jul 2013, 00:59
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16031
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

04 Dec 2014, 12:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Current Student
Joined: 04 May 2015
Posts: 75
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

13 Jul 2015, 11:51
Bunuel wrote:
rxs0005 wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

I got a bit tripped up in the wording here. I made the assumption that you could choose the same letter twice and got myself all sorts of confused. But after reading the OA it makes a lot of sense and hope I don't make these sorts of stupid mistakes in the future... sigh
_________________

If you found my post useful, please consider throwing me a Kudos... Every bit helps

Manager
Joined: 08 Jan 2015
Posts: 93
Location: Thailand
Schools: Duke '19 (A), HKU (A)
GMAT 1: 540 Q41 V23
GMAT 2: 570 Q44 V24
GMAT 3: 550 Q44 V21
GMAT 4: 660 Q48 V33
GPA: 3.31
WE: Science (Other)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

20 Jul 2015, 22:22
How do we know that we can't use the same letter twice?
Verbal Forum Moderator
Joined: 29 Apr 2015
Posts: 897
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

21 Jul 2015, 23:04
Bunuel wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

Could we also solve this with: Total Combinations - Forbidden Combinations?

Total = 5*4*3 = 60
Forbidden (A is not part): 4*3*2 = 24
Forbidden (B is not part): 4*3*2 = 24
Forbidden (A and B are not part): 3*2*1 = 6

Total Forbidden Combinations: 54, Answer 6

I know its wrong but where is my mistake?
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Verbal Forum Moderator
Joined: 29 Apr 2015
Posts: 897
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

19 Aug 2015, 13:06
Aves wrote:
How do we know that we can't use the same letter twice?

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Verbal Forum Moderator
Joined: 29 Apr 2015
Posts: 897
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

19 Aug 2015, 13:19
rxs0005 wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

If one visualises this step by step:

Attachment:

STEP BY STEP.jpg [ 12.52 KiB | Viewed 1422 times ]

With the first step you just ask yourself how many different arrangements there are of 3 Letters? As bunuel calcualted this is simply 3! = 6
Then the constraints; put everything in so called "selection-boxes" and ask yourself, how many possible combinations does the first letter have, the second, and the last if A and E must be among the selected. Finally multiply with 6.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Intern
Joined: 02 Jun 2015
Posts: 33
Location: United States
Concentration: Operations, Technology
GMAT Date: 08-22-2015
GPA: 3.92
WE: Science (Other)
How many different arrangements of letters are possible if [#permalink]

### Show Tags

19 Aug 2015, 18:04
1
KUDOS
reto wrote:
Could we also solve this with: Total Combinations - Forbidden Combinations?

Total = 5*4*3 = 60
Forbidden (A is not part): 4*3*2 = 24
Forbidden (B is not part): 4*3*2 = 24
Forbidden (A and B are not part): 3*2*1 = 6

Total Forbidden Combinations: 54, Answer 6

I know its wrong but where is my mistake?

Yes, you can do it this way. You are correct in all of your calculations, but you are double counting in your statements.

It should be like this:
Total = 5*4*3 = 60
Forbidden (A is not part of, but B is): 3*3*2 = 18
Forbidden (B is not part of, but A is): 3*3*2 = 18
Forbidden (Both A and B are not part of): 6

Total Forbidden Combinations = 42, Answer 6

You should be able to see where your problem is from this. =)
Current Student
Joined: 09 Aug 2015
Posts: 95
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

20 Aug 2015, 18:08
reto wrote:
Bunuel wrote:
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

Could we also solve this with: Total Combinations - Forbidden Combinations?

Total = 5*4*3 = 60
Forbidden (A is not part): 4*3*2 = 24
Forbidden (B is not part): 4*3*2 = 24
Forbidden (A and B are not part): 3*2*1 = 6

Total Forbidden Combinations: 54, Answer 6

I know its wrong but where is my mistake?[/quote]

Hey there,

note that the formula from set theorey is Total - X - Y + [X AND Y].

you actually need to add 6 combinations back.
CEO
Joined: 17 Jul 2014
Posts: 2525
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

07 Feb 2016, 09:51
I kind of got to the right answer differently...
we have:
A B C D E
5 letters.
we can thus select 3 out of 5 in: 5x4x3 ways. this is 60. Since the place of A and E is not important, we can divide by 2!, or 30 ways. Now, it must be true that we should have a number of combinations that is less than 30, because in 5x4x3 we have all combinations, including those in which A and E are not. so D looks fine.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16031
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

16 Mar 2017, 18:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 05 Jan 2017
Posts: 436
Location: India
Re: How many different arrangements of letters are possible if [#permalink]

### Show Tags

17 Mar 2017, 00:36
If A and E has to be selected. all we have to do is select 1 from B,C,D. No. of ways = 3C1

arranging these three selected= 3!

therefore total ways = 3C1 x 3! = 18

Option D
Re: How many different arrangements of letters are possible if   [#permalink] 17 Mar 2017, 00:36
Similar topics Replies Last post
Similar
Topics:
3 How many different arrangements of letters are possible, if three lett 4 06 Apr 2017, 09:33
4 How many different arrangements are possible to place seven different 3 17 Nov 2016, 18:26
How many 2 letter arrangements possible with "EELL"? 8 30 Jun 2015, 07:48
8 How many different arrangements of A, B, C, D, and E are possible 8 27 May 2016, 10:46
9 How many different possible arrangements can be obtained from the lett 6 19 Mar 2016, 12:04
Display posts from previous: Sort by