Last visit was: 19 Nov 2025, 08:03 It is currently 19 Nov 2025, 08:03
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,389
Own Kudos:
778,260
 [11]
Given Kudos: 99,977
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: 105,389
Kudos: 778,260
 [11]
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 23 Feb 2021, 03:30
Kudos
Add Kudos
11
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:

75% (hard)

Question Stats:

54% (02:13) correct 46% (02:21) wrong based on 169 sessions

History

Date
Time
Result
Not Attempted Yet
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which reads the same backwards and forwards, is

(A) 6
(B) 8
(C) 10
(D) 12
(E) 14


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
ShowHide Answer
Official Answer
C
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 19 Nov 2025
Posts: 547
Own Kudos:
1,114
 [3]
Given Kudos: 13
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert
Expert reply
GMAT 1: 750 Q51 V39
Posts: 547
Kudos: 1,114
 [3]
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 23 Feb 2021, 03:43
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
There are 5 As - so 2 on either side and one A in the middle
There are 6 Bs - so 3 on either side

So there are 5 letters on the left and 5 on the right with one A in the middle

Number of arrangements on the left side
= 5!/(2! x 3!) = 10

We just need to check the arrangements on one side since each arrangement on the left must mirror the same arrangement on the right.

Hence, there are 10 ways.
Answer C

Posted from my mobile device
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 19 Nov 2025
Posts: 6,839
Own Kudos:
16,351
 [2]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,839
Kudos: 16,351
 [2]
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 23 Feb 2021, 03:51
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which reads the same backwards and forwards, is

(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Show more

- We have to arrange the 11 letters (5 A’ and 6 B’s)

- The arrangement must be palindrome which read same backwards and forwards

- For the result of 11 letters to be palindrome, one letter must be pivoted at 6th place - - - - - - - - - - -

- The pivoted letter MUST be an A because there are 5 A's so we can't divide them into two equal parts for result to be palindrome
- - - - - A - - - - -

- Now our objective is only to arrange the 5 letters to the left of middle letter as an arrangement to the left will be mirrored as arrangemenbt to teh right of pivoted letter
- - - - - A - - - - -

- The 5 letter to the left, must be 2 A's and 3 B's

- Arrangements of 2 A's and 3 B's can be counted in 5C2 ways because we only need to identify the two places for 2 A's out of 5 empty places.
- No arrangement need to be taken into account because all A's are identical and all B's are identical

So desired outcomes = \(^5C_2 = 10\)



Answer: Option C
avatar
TarunKumar1234
avatar
Joined: 14 Jul 2020
Last visit: 28 Feb 2024
Posts: 1,107
Own Kudos:
1,348
Given Kudos: 351
Location: India
Posts: 1,107
Kudos: 1,348
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 13 Mar 2021, 00:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which reads the same backwards and forwards, is

There are total 11 places to fill, for symmetry, we need to fill middle place first.
We have A = odd number, so one A will be in between and 2 As on left and 2 As on right side.
B = 3 left side and 3 right side

So, required combination = 5!/(2!*3!) =10 ways

I think C. :)
User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,350
Own Kudos:
742
Given Kudos: 1,656
Posts: 1,350
Kudos: 742
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 08 Sep 2021, 08:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3 minutes to Brute Force this baby with a little bit of logic attached. Looking forward to looking at the more effective ways of solving this problem

(1st) because we have 11 spaces and 5 A's and 6 B's - in order for the Letters to read the Same Backwards and Forwards, we MUST make the Median Letter (6th Space) the Letter A. if we make the 6th Letter B, then the best we can hope for is to have 3 A's on one side of the Median and 2 A's on the other side of the Median. We simply will not have enough A's and B' to have to arrangement read the same forwards and backwards.

Because there is 1 Less A, we can never get an arrangement to read the same backwards and forwards if the Letter B occupies the 6th spot out of of the 11 total spots.


(2nd)whatever we choose for spot 1 -----> must be the SAME Letter for spot 11.

thus, once we have chosen a Letter for spot 1 ------> spot 11 MUST automatically contain that Letter

the same logic applies to: Spots 2 and 10 ; Spots 3 and 9 ; Spots 4 and 8 ; Spots 5 and 7

so we can start out with A in the 6th spot and we need to examine ONLY the first 5 spots to determine the no. of possibilities (b/c once we choose these spots, the last 5 spots will automatically be chosen.

__ ; ___ ; ___ ; ___ ; ___ ; A


furthermore, since we have 5 A's and 6 B's:

we must have 2 A's and 3 B's occupy these first 5 spots so that we have an equivalent number of 2 A's and 3 B's in the slots 7 through 11, inclusive, and can have an arrangement that reads the same forwards and backwards.


(3rd)Brute Force the possibilities

Start with: B -- B -- B -- A -- A ----> 1 way

then we can shift 1 A to the Left: B -- B -- A -- B -- A

now we can find all the possibilities with the FIRST 3 Letters being 'B - B- A": the A and B can switch places ---> 2! = 2 ways


then, we can shift the A to the Left Again: B -- A-- B -- B -- A

at this point, we can find all the possibilities with the FIRST 2 Letters being: B -- A

the second 3 Letters can be arranged in: 3!/2! = 3 ways



then, we can shift the A to the Left Again so that the first letter is A: A -- B -- B -- B --- A

we can find all the possibilities with the FIRST 2 Letters being: A -- B

the second 3 Letters can be arranged in: 3!/2! = 3 ways


LAST Arrangement not counted: First 2 Letters being: A - A

A - A - B - B - B -----------> 1 way


Total Number of Arrangements = 1 + 2 + 3 + 3 + 1 = 10 Total Ways



Answer: 10
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
Number of ways in which 5 A’ and 6 B’s can be arranged in a row which 09 May 2025, 04:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105389 posts
Krunaal
Tuck School Moderator
805 posts