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# A rectangular floor measure 2 by 3 meters, there are 5

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Manager
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A rectangular floor measure 2 by 3 meters, there are 5 [#permalink]

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12 Aug 2006, 17:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A rectangular floor measure 2 by 3 meters, there are 5 white, 5 red and 5 black parquet blocks available. Each block measurers 1 by 1 meter. In how many different color patterns can the floor be pargueted.

a)104
b)213
c)577
d)705
e)726
Senior Manager
Joined: 21 Jun 2006
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12 Aug 2006, 19:28
5 w, 5b, 5 r = 15 alltogether
total reqd = 2*3 = 6
15C6 combinations..
Can anyone please explain further, I'm stumped?
GMAT Instructor
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13 Aug 2006, 03:40
Clue: It would be a much easier question of there were 6 tiles of each colour available...Each of the six spaces could be filled 3 ways
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13 Aug 2006, 06:59
rkatl wrote:
A rectangular floor measure 2 by 3 meters, there are 5 white, 5 red and 5 black parquet blocks available. Each block measurers 1 by 1 meter. In how many different color patterns can the floor be pargueted.

a)104
b)213
c)577
d)705
e)726

how about 3x3x3x3x3x3 -3 =729-3 = 726
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13 Aug 2006, 08:47
E

Rectangular floor consists of six 1 by 1 block.

Each block can either white or red or black.

So the required combinations= 3*3*3*3*3*3= 729

but this also includes when all the blocks are either white or black or red which is not possible
so we need to subtract 3 possible cases.

729-3= 726
Senior Manager
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13 Aug 2006, 18:09
Thanks for the answers.. i guess it is just a simple combination questions.
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11 Dec 2007, 13:47
AK wrote:
E

Rectangular floor consists of six 1 by 1 block.

Each block can either white or red or black.

So the required combinations= 3*3*3*3*3*3= 729

but this also includes when all the blocks are either white or black or red which is not possible
so we need to subtract 3 possible cases.

729-3= 726

we have 6 slots. there are 3 colors to choose from to fill each of these slots

(3c1)^6 = 729

i still do not understand how the subtraction of 3 is accounted for.
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11 Dec 2007, 13:55
bmwhype2 wrote:
AK wrote:
E

Rectangular floor consists of six 1 by 1 block.

Each block can either white or red or black.

So the required combinations= 3*3*3*3*3*3= 729

but this also includes when all the blocks are either white or black or red which is not possible
so we need to subtract 3 possible cases.

729-3= 726

we have 6 slots. there are 3 colors to choose from to fill each of these slots

(3c1)^6 = 729

i still do not understand how the subtraction of 3 is accounted for.

nevermind, figured it out.
Intern
Joined: 25 Nov 2007
Posts: 38
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11 Dec 2007, 16:35
bmwhype2 wrote:
AK wrote:
E

Rectangular floor consists of six 1 by 1 block.

Each block can either white or red or black.

So the required combinations= 3*3*3*3*3*3= 729

but this also includes when all the blocks are either white or black or red which is not possible
so we need to subtract 3 possible cases.

729-3= 726

we have 6 slots. there are 3 colors to choose from to fill each of these slots

(3c1)^6 = 729

i still do not understand how the subtraction of 3 is accounted for.

Because there are only 5 blocks , so we can have 6 of same color. I like this question..
11 Dec 2007, 16:35
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