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## 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:
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#### 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

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

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### GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
610 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.

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### GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
610 members
1710
GMAT Score:
800
Wed Jan 30, 2008 7:52 pm
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.

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sibbineni Master | Next Rank: 500 Posts
Joined
04 Jan 2008
Posted:
222 messages
15
Wed Jan 30, 2008 7:56 pm
I agree with stuart

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

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