• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

combinations

This topic has 2 expert replies and 3 member replies
Nidhs Senior | Next Rank: 100 Posts
Joined
06 Jan 2008
Posted:
69 messages
Followed by:
1 members
3

combinations

Wed Jan 30, 2008 7:35 pm
How many different ways can 3 cubes be painted if each cube is painted one color and only 3 colors red, blue, green are available? ( order is not considered, for example green, green blue is condidered the same as green, blue, green.)
a)2 b)3 c) 9 d)10 e) 27

can someone please expain to me a shorter method of solving this other than listing the orders down

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
608 members
1710
GMAT Score:
800
Tue Jun 29, 2010 9:21 am
ayushiiitm wrote:
Should it not be 3*3*3

because we may say
for first cube we have 3 choice, for second we have 3 and third we have 3
Hi!

The problem with your approach is that you've included duplicates.

For example, you've counted:

RGB
RBG
GRB
GBR
BRG
BGR

as 6 different combinations, even thought they're all the same (one of each colour).

Since order doesn't matter in this question (we just want to know the colours of the cubes, we don't care in what order we painted them), you have to use a different counting method.

Thanked by: ayushiiitm
Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
ayushiiitm Master | Next Rank: 500 Posts
Joined
23 Jul 2008
Posted:
216 messages
5
Test Date:
2nd August 2010
Target GMAT Score:
760
GMAT Score:
700
Tue Jun 29, 2010 9:35 am
Stuart Kovinsky wrote:
ayushiiitm wrote:
Should it not be 3*3*3

because we may say
for first cube we have 3 choice, for second we have 3 and third we have 3
Hi!

The problem with your approach is that you've included duplicates.

For example, you've counted:

RGB
RBG
GRB
GBR
BRG
BGR

as 6 different combinations, even thought they're all the same (one of each colour).

Since order doesn't matter in this question (we just want to know the colours of the cubes, we don't care in what order we painted them), you have to use a different counting method.
Thanks Stuart

_________________
Success is a journey.....enjoy every moment of it

GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
608 members
1710
GMAT Score:
800
Tue Jun 29, 2010 9:21 am
ayushiiitm wrote:
Should it not be 3*3*3

because we may say
for first cube we have 3 choice, for second we have 3 and third we have 3
Hi!

The problem with your approach is that you've included duplicates.

For example, you've counted:

RGB
RBG
GRB
GBR
BRG
BGR

as 6 different combinations, even thought they're all the same (one of each colour).

Since order doesn't matter in this question (we just want to know the colours of the cubes, we don't care in what order we painted them), you have to use a different counting method.

Thanked by: ayushiiitm
Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
ayushiiitm Master | Next Rank: 500 Posts
Joined
23 Jul 2008
Posted:
216 messages
5
Test Date:
2nd August 2010
Target GMAT Score:
760
GMAT Score:
700
Tue Jun 29, 2010 9:35 am
Stuart Kovinsky wrote:
ayushiiitm wrote:
Should it not be 3*3*3

because we may say
for first cube we have 3 choice, for second we have 3 and third we have 3
Hi!

The problem with your approach is that you've included duplicates.

For example, you've counted:

RGB
RBG
GRB
GBR
BRG
BGR

as 6 different combinations, even thought they're all the same (one of each colour).

Since order doesn't matter in this question (we just want to know the colours of the cubes, we don't care in what order we painted them), you have to use a different counting method.
Thanks Stuart

_________________
Success is a journey.....enjoy every moment of it

ayushiiitm Master | Next Rank: 500 Posts
Joined
23 Jul 2008
Posted:
216 messages
5
Test Date:
2nd August 2010
Target GMAT Score:
760
GMAT Score:
700
Tue Jun 29, 2010 2:05 am
Stuart Kovinsky wrote:
Consider 3 scenarios:

(1) all 3 the same colour... 3 options
(2) all 3 different colours... 1 option
(3) 2 of 1 colour and 1 of another colour (so we're using 2 of the 3 colours): 3C2 gives us the possible 2 colour choices. However, we need to double it, since if we choose R and B we could have RRB or RBB.

So, 3C2 * 2 = 3 * 2 = 6

3 + 1 + 6 = 10 possibilities.
Should it not be 3*3*3

because we may say
for first cube we have 3 choice, for second we have 3 and third we have 3

_________________
Success is a journey.....enjoy every moment of it

Best Conversation Starters

1 lheiannie07 112 topics
2 swerve 64 topics
3 LUANDATO 64 topics
4 ardz24 61 topics
5 AAPL 57 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

227 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

176 posts
3 Jeff@TargetTestPrep

Target Test Prep

168 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

138 posts
5 GMATGuruNY

The Princeton Review Teacher

129 posts
See More Top Beat The GMAT Experts