Last visit was: 23 Apr 2026, 07:15 It is currently 23 Apr 2026, 07:15
Home
Messages
Tests
Schools
Events
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,782
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,778
Kudos: 810,782
How many different arrangements of the letters A, B, C, D, and E are 26 Dec 2016, 11:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

93% (00:42) correct 7% (01:36) wrong based on 123 sessions

History

Date
Time
Result
Not Attempted Yet
How many different arrangements of the letters A, B, C, D, and E are possible where A occupies the middle position and all letters must be used?

A. 60
B. 48
C. 24
D. 12
E. 6
ShowHide Answer
Official Answer
C
avatar
[email protected]
avatar
Joined: 30 Oct 2016
Last visit: 13 Sep 2017
Posts: 4
Own Kudos:
4
Given Kudos: 68
Posts: 4
Kudos: 4
How many different arrangements of the letters A, B, C, D, and E are 26 Dec 2016, 21:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
4[u] 3 a 2 1[/u]
24
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,903
Own Kudos:
5,452
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,903
Kudos: 5,452
How many different arrangements of the letters A, B, C, D, and E are 27 Dec 2016, 09:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
How many different arrangements of the letters A, B, C, D, and E are possible where A occupies the middle position and all letters must be used?

A. 60
B. 48
C. 24
D. 12
E. 6
Show more

__ __ A __ __

The first place can be filled by B,C,D or E - In 4 ways
The Second place can be filled by B,C,D or E - In 3 ways
The Fourth place can be filled by B,C,D or E - In 2 ways
The Fifth place can be filled by B,C,D or E - In 1 way

So, The total No of ways will be 4*3*2*1 = 24 ways...

Correct answer will definitely be (C) 24
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,868
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,868
How many different arrangements of the letters A, B, C, D, and E are 27 Dec 2016, 09:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let us use the counting spaces method to solve this question.

2 key things to note here.
    1. The third place is filled by the letter "A", so we have only 4 places left to fill
    2. There are no constraints on the letters that can occupy these 4 places. Hence, we can use any letter to fill any place.


The first place can be filled in 4 ways. We can chose any one of the four lettters - B, C, D or E.
On doing so we are left with only 3 choices for the second place. Similarly, on filling the second place, we will be left with only 2 choices to fill the fourth place and only one way to fill the last place.

Hence, the total number of arrangements = \(4*3*2*1=24\). Correct answer is Choice C.
Moderators:
Bunuel
Math Expert
109778 posts
Krunaal
Tuck School Moderator
853 posts