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Nidhs: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sun Jan 06, 2008 7:12 pm; Thanked: 3 times; Followed by:1 members

combinations

by Nidhs » 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

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Source: Beat The GMAT — Problem Solving | Wed Jan 30, 2008 7:35 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » 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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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sibbineni: Master | Next Rank: 500 Posts; Posts: 222; Joined: Fri Jan 04, 2008 8:10 pm; Thanked: 15 times

by sibbineni » Wed Jan 30, 2008 7:56 pm

I agree with stuart

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ayushiiitm: Master | Next Rank: 500 Posts; Posts: 216; Joined: Wed Jul 23, 2008 2:35 am; Location: Pune, India; Thanked: 5 times; GMAT Score:700

by ayushiiitm » 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

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » 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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ayushiiitm: Master | Next Rank: 500 Posts; Posts: 216; Joined: Wed Jul 23, 2008 2:35 am; Location: Pune, India; Thanked: 5 times; GMAT Score:700

by ayushiiitm » 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