Last visit was: 23 Apr 2026, 13:07 It is currently 23 Apr 2026, 13:07
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
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,872
 [28]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,872
 [28]
How many different flags can be made from4 colors- Red, Blue, Green, a Updated on: 13 Aug 2018, 07:08
Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:16.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:08, edited 6 times in total.
Kudos
Add Kudos
28
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

49% (01:56) correct 51% (01:29) wrong based on 585 sessions

History

Date
Time
Result
Not Attempted Yet
Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #3

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

Learn to use the Keyword Approach in Solving PnC question from the following article:


Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,002
 [6]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,002
 [6]
How many different flags can be made from4 colors- Red, Blue, Green, a 12 Apr 2018, 00:53
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
EgmatQuantExpert
Learn structured approach to identify permutation and combination question - Exercise Question #2

How many different flags can be made from4 colors- Red, Blue, Green, and White?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64
Show more

The question is incomplete the way it is..

1) I would say - " different flags from 20 m cloth if one flag is .....", so it should be different types of flags..
I am sure it means this so we can leave it here..
2) If I use two colors also, I can make 100s of different types of flags..

so the question could have been two ways..

A) "How many different types of flags can be made from using atleast one of 4 colors- Red, Blue, Green, and White" - Without any restrictions
so a COMBINATION question..
one colour - 4 ways
two colours - 4C2 - 6 ways
three colour - 4C3 - 6 ways
four colour - 4C4 - 1 way

total = 17 ways

B) "How many different types of flags can be made from using atleast one of 4 colors - Red, Blue, Green, and White -in horizontal stripe/vertical stripes, each coloured being used once" - With restrictions
so a PERMUTATION question..
one colour - 4 ways
two colours - 4P2 - 6*2=12 ways
three colour - 4P3 - 6*3!=24 ways
four colour - 4P4 - 4*3*2*1=24 way

total = 64 ways
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,235
 [6]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,235
 [6]
How many different flags can be made from4 colors- Red, Blue, Green, a 11 Apr 2018, 23:44
2
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
EgmatQuantExpert
Learn the structured approach to identify permutation and combination question - Exercise Question #2

How many different flags can be made from4 colors- Red, Blue, Green, and White?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64
Show more


There are 4 different colors which can be used to make the flags.

When there is 1 color in the flag - 4 possibilities
When there are 2 colors in the flag - 4*3 = 12 possibilities
When there are 3 colors in the flag - 4*3*2 = 24 possibilities
When there are 4 colors in the flag - 4*3*2*1 = 24 possibilities

Therefore, there are a total of 4+12+24+24 = 64 possibilities(Option E) in which the flags can be made.
General Discussion
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,872
 [1]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,872
 [1]
How many different flags can be made from4 colors- Red, Blue, Green, a 17 Apr 2018, 08:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Given:
• We have 4 colours- Red, Blue, Green, and White to form the flag.

To find:
• The number of ways we can form different flags from the 4 colours available.

Approach and Working:

    • From the 4 colors available, we can form 4 different types of flag:
    o Flag with single color
    o Flag with two colors
    o Flag with three colors
    o Flag with four colors

• Hence, total number of flags= Flag with one color +Flag with two colors + Flag with three colors+ Flag with four colors

Flag with one color:

From 4 colors, we can select 1 color to form the flag in \(^4c_1\)=4 ways.

Flag with more than one colors:

Since the order of colour matters in a flag, this is a case of permutation.
    • Thus, total number of flags with two colours= \(^4P_2\)=2
    • In the similar fashion, total number of flags with three colours and four colours = \(^4P_3\)= 24 and \(^4P_4\)=24 ways respectively.

Thus, total number of flags= 4+12+24+24= 64

Hence, option E is the correct answer.

Answer: E
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,872
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,872
How many different flags can be made from4 colors- Red, Blue, Green, a 17 Apr 2018, 09:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey chetan2u,

Apology for the inconvenience.

We have updated the question.

Regards
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 23 Apr 2026
Posts: 22,283
Own Kudos:
26,531
 [1]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,531
 [1]
How many different flags can be made from4 colors- Red, Blue, Green, a 09 Dec 2019, 18:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #3

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

Learn to use the Keyword Approach in Solving PnC question from the following article:

Show more

The number of flags that can be made using only 1 color is 4P1 = 4.

The number of flags that can be made using exactly 2 colors is 4P2 = 4 x 3 = 12.

The number of flags that can be made using exactly 3 colors is 4P3 = 4 x 3 x 2 = 24.

The number of flags that can be made using all 4 colors is 4P4 = 4 x 3 x 2 x 1 = 24.

Therefore, the total number of flags that can be made is 4 + 12 + 24 + 24 = 64.

Answer: E.
User avatar
Sanyami19
User avatar
Joined: 02 Oct 2021
Last visit: 05 Nov 2022
Posts: 12
Own Kudos:
1
Given Kudos: 163
Posts: 12
Kudos: 1
How many different flags can be made from4 colors- Red, Blue, Green, a 03 Oct 2022, 07:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert

Solution



Given:
• We have 4 colours- Red, Blue, Green, and White to form the flag.

To find:
• The number of ways we can form different flags from the 4 colours available.

Approach and Working:

    • From the 4 colors available, we can form 4 different types of flag:
    o Flag with single color
    o Flag with two colors
    o Flag with three colors
    o Flag with four colors

• Hence, total number of flags= Flag with one color +Flag with two colors + Flag with three colors+ Flag with four colors

Flag with one color:

From 4 colors, we can select 1 color to form the flag in \(^4c_1\)=4 ways.

Flag with more than one colors:

Since the order of colour matters in a flag, this is a case of permutation.
    • Thus, total number of flags with two colours= \(^4P_2\)=2
    • In the similar fashion, total number of flags with three colours and four colours = \(^4P_3\)= 24 and \(^4P_4\)=24 ways respectively.

Thus, total number of flags= 4+12+24+24= 64

Hence, option E is the correct answer.

Answer: E
Show more


Hi, what is the inference of the phrase - "no colour is repeated more than once?". Does it mean a) no colour is used more than once, in which case the above solution applies or b) each colour can be repeated only 1? In this scenario, no. of flags with 2 colours will be equal to 16. and so on and so forth for # of flags with 3 and 4 colours.
Please suggest how the usage of word repeated has to be understood, in GMAT context?
User avatar
RockoGmat
User avatar
Joined: 01 Jul 2025
Last visit: 19 Apr 2026
Posts: 168
Own Kudos:
19
 [1]
Given Kudos: 84
Posts: 168
Kudos: 19
 [1]
How many different flags can be made from4 colors- Red, Blue, Green, a 01 Nov 2025, 02:48
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I don't prefer getting into permutations so I did it this way.

Only 1 colour -> 4 ways (no arrangement possible, only 1)

2 colours -> 2! x 4C2 = 12 ways

3 colours -> 3! x 4C3 = 6 x 4 = 24 ways

4 colours -> 4! x 1 = 24 ways

Total ways = 4+12+24+24 = 64 ways

Can be solved in under 90 seconds this way.

Hit kudos if you liked my approach/solution!
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts