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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many different arrangements of letters are possible if [#permalink]

Show Tags

27 Nov 2010, 07:49

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

59% (01:07) correct
41% (01:15) wrong based on 350 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?

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.

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.

Answer: D.

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
_________________

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.

Answer: D.

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.

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.
_________________

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.

Answer: D.

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

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.

Answer: D.[/quote]

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.

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 1805 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.

How many different arrangements of letters are possible if [#permalink]

Show Tags

19 Aug 2015, 18:04

1

This post received 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. =)

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.

Answer: D.

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].

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.

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.
_________________

Re: How many different arrangements of letters are possible if [#permalink]

Show Tags

02 Aug 2017, 03:46

ABCDE can be arranged as BCD & AE [default selection]. So BCD can be selected in 3C1=3 ways and this should be arranged [either B,C or D] among-st each other in 3P3=6 ways. So final ways should be 3*6=18. Option D.

Re: How many different arrangements of letters are possible if [#permalink]

Show Tags

02 Aug 2017, 03:52

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

In such questions, first satisfy the requirements of the problem, in this case by picking A and E from the lot. The question is transformed to selecting 1 letter from B, C, and D and then arranging 3 distinct letters. Hence the number of arrangements = 3*3!=18