Last visit was: 24 Apr 2026, 19:12 It is currently 24 Apr 2026, 19:12
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
805+ (Hard)|   Combinations|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,087
 [13]
Given Kudos: 105,873
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: 109,818
Kudos: 811,087
 [13]
A cameraman wants to arrange six students of six different heights for 02 Oct 2018, 01:53
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

34% (02:16) correct 66% (02:33) wrong based on 140 sessions

History

Date
Time
Result
Not Attempted Yet
A cameraman wants to arrange six students of six different heights for a picture by placing them in two rows of three such that each student in the first row stands in front of a student in the second row. The heights of the students within each row must increase from left to right, and each student in the second row must be taller than the student standing in front of him. How many such arrangements of the six students are possible?

(A) 4
(B) 5
(C) 6
(D) 12
(E) 24
ShowHide Answer
Official Answer
B
User avatar
AvidDreamer09
User avatar
Joined: 19 Apr 2017
Last visit: 14 Aug 2025
Posts: 79
Own Kudos:
147
 [1]
Given Kudos: 40
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE:Operations (Hospitality and Tourism)
Schools: ESSEC '22
Posts: 79
Kudos: 147
 [1]
A cameraman wants to arrange six students of six different heights for 05 Oct 2018, 11:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IF 1 is the shortest and 6 is the tallest.
1 has to be on the first row left and 2 has to be on the second row right so their position is fixed
_ _ 6
1 _ _

To make this simpler arrange the ways in which the first row can be arranged apart from 1

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

Possible combinations for the first row 23, 24, 25,34,35 so answer 5
User avatar
Anurag06
User avatar
Joined: 10 Dec 2019
Last visit: 23 Mar 2020
Posts: 40
Own Kudos:
6
 [1]
Given Kudos: 15
Posts: 40
Kudos: 6
 [1]
A cameraman wants to arrange six students of six different heights for 04 Feb 2020, 03:23
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
AvidDreamer09
IF 1 is the shortest and 6 is the tallest.
1 has to be on the first row left and 2 has to be on the second row right so their position is fixed
_ _ 6
1 _ _

To make this simpler arrange the ways in which the first row can be arranged apart from 1

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

Possible combinations for the first row 23, 24, 25,34,35 so answer 5
Show more


Hi

Can you please explain this step ?

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

I couldn't quite grasp it considering the above 2 restrictions on either ends.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,087
 [1]
Given Kudos: 105,873
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: 109,818
Kudos: 811,087
 [1]
A cameraman wants to arrange six students of six different heights for 04 Feb 2020, 03:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Anurag06
AvidDreamer09
IF 1 is the shortest and 6 is the tallest.
1 has to be on the first row left and 2 has to be on the second row right so their position is fixed
_ _ 6
1 _ _

To make this simpler arrange the ways in which the first row can be arranged apart from 1

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

Possible combinations for the first row 23, 24, 25,34,35 so answer 5


Hi

Can you please explain this step ?

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

I couldn't quite grasp it considering the above 2 restrictions on either ends.
Show more

We have two conditions to meet:
1. The heights of the students within each row must increase from left to right
2. Each student in the second row must be taller than the student standing in front of him.

For example, 3 - 2, won't be valid according to 1 and 4 - 5, in the first row won't be valid according to 2 (there are no two students taller than they are to stand behind them in the second row)
User avatar
Anurag06
User avatar
Joined: 10 Dec 2019
Last visit: 23 Mar 2020
Posts: 40
Own Kudos:
6
Given Kudos: 15
Posts: 40
Kudos: 6
A cameraman wants to arrange six students of six different heights for 04 Feb 2020, 04:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Anurag06
AvidDreamer09
IF 1 is the shortest and 6 is the tallest.
1 has to be on the first row left and 2 has to be on the second row right so their position is fixed
_ _ 6
1 _ _

To make this simpler arrange the ways in which the first row can be arranged apart from 1

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

Possible combinations for the first row 23, 24, 25,34,35 so answer 5


Hi

Can you please explain this step ?

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54
45(4 will be ahead of 3 or 2)

I couldn't quite grasp it considering the above 2 restrictions on either ends.

We have two conditions to meet:
1. The heights of the students within each row must increase from left to right
2. Each student in the second row must be taller than the student standing in front of him.

For example, 3 - 2, won't be valid according to 1 and 4 - 5, in the first row won't be valid according to 2 (there are no two students taller than they are to stand behind them in the second row)
Show more

Thank you Bunuel. :)

I had not considering ranking system from 1 to 6 which will be low to high respectively.

Second mistake was regarding 32 as it would violate left to right order in row of shorter people.
avatar
judsonvpires
avatar
Joined: 02 Dec 2017
Last visit: 18 Feb 2020
Posts: 2
Own Kudos:
1
Given Kudos: 56
Posts: 2
Kudos: 1
A cameraman wants to arrange six students of six different heights for 04 Feb 2020, 07:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Could someone post an alternative explanation? Perhaps with or referencing the combinations formula? I'm not sure how to translate the restricitons on that formula. Thank you in advance.
User avatar
Anurag06
User avatar
Joined: 10 Dec 2019
Last visit: 23 Mar 2020
Posts: 40
Own Kudos:
6
Given Kudos: 15
Posts: 40
Kudos: 6
A cameraman wants to arrange six students of six different heights for 04 Feb 2020, 07:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
judsonvpires
Could someone post an alternative explanation? Perhaps with or referencing the combinations formula? I'm not sure how to translate the restricitons on that formula. Thank you in advance.
Show more

_ _ 6 (taller height)
1 _ _ (shorter height)
2 3
2 4
2 5
3 4
3 5

Except this five if you inter change any values then considering from 1 (extreme shortest) to 6 (extreme tallest) you would violate condition 1 and since it is mentioned the above row here would be always *higher* and below row as *lower* in terms of height comparison.
i.e. _ _ 6 (shown above) if you use another value, then it would violate second condition.

Try plugging different values and check yourself. Hope this helps!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
A cameraman wants to arrange six students of six different heights for 10 Oct 2025, 09:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts