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How many different ways can 3 cubes be painted if each cube is painted

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How many different ways can 3 cubes be painted if each cube is painted [#permalink]

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New post 18 Apr 2017, 04:54
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How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?

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Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

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New post 18 Apr 2017, 05:04
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stonecold wrote:
How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?


XXX - 3 cases (red, red, red; green, green, green; blue, blue, blue)

XXY - \(C^1_3*2 = 6\), where \(C^1_3\) is the number of ways to choose which color will be used for two identical colored cubes (XX) and *2 because there will be 2 colors left to choose from for Y.

XYZ - 1 case (red, green, blue)

3 + 6 + 1 = 10.

Answer: B.
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Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

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New post 18 Apr 2017, 05:14
stonecold wrote:
How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?



Hi..

Yes picking up indl cases would be better easier and less error prone.
1) all of same colour-3
2) two of same colour..
Two colours can be choosen in 3C2=3!/2!=3 ways and any of these two can be on TWO cubes. So 3*2=6
3) all of one colour-1..

Total -- 3+6+1=10
B
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Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

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New post 25 Aug 2017, 05:21
Hi Bunuel

Can you please me why this approach cannot be used.

1st cube can be painted in 3 ways. Same with 2nd and 3rd.

So total 3*3*3 = 27 ways.
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Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

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New post 25 Aug 2017, 05:55
gauravraos wrote:
Hi Bunuel

Can you please me why this approach cannot be used.

1st cube can be painted in 3 ways. Same with 2nd and 3rd.

So total 3*3*3 = 27 ways.


We are told that "Order is not considered, for example green,green,blue is considered the same as green blue green)". Among other duplications, your approach will give for example {red, green, blue} as well as {blue, red, green} or {red, green, green} as well as {green, green, red}.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: How many different ways can 3 cubes be painted if each cube is painted   [#permalink] 25 Aug 2017, 05:55
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