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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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18 Apr 2017, 04:54
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Difficulty:

95% (hard)

Question Stats:

35% (02:09) correct 65% (01:46) wrong based on 67 sessions

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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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Joined: 02 Sep 2009
Posts: 54434
Re: How many different ways can 3 cubes be painted if each cube is painted  [#permalink]

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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.

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

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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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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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Posts: 54434
Re: How many different ways can 3 cubes be painted if each cube is painted  [#permalink]

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

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