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# a rectangular floor measures 2 by 3 meters. there are 5

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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 390 [0], given: 4

a rectangular floor measures 2 by 3 meters. there are 5 [#permalink]  05 Nov 2007, 08:49
a rectangular floor measures 2 by 3 meters.
there are 5 white, 5 black and 5 yellow parquet blocks available.
Each block measures 1*1 meter.
In how many different color patterns can the floor be parqueted?
Senior Manager
Joined: 06 Mar 2006
Posts: 497
Followers: 7

Kudos [?]: 92 [0], given: 1

ok, the area of the floor is 2*3=6 and the area of each block is 1*1=6
so there must be 6 blocks total.
As for the color combination; there are 3 different colors
For the first block, there will be 3 choice
2nd block, three color choice
3rd, 4th, and 5th all have 3 color choice
the 6th one will end up with 2 color choice because each color has only 5 pieces.
So it will be 3*3*3*3*3*2=486 different color patterns.
Manager
Joined: 01 Nov 2007
Posts: 83
Followers: 0

Kudos [?]: 4 [0], given: 0

How would you solve this with Permutation/Combination?

Thanks
Director
Joined: 09 Aug 2006
Posts: 763
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Kudos [?]: 77 [0], given: 0

Re: Area [#permalink]  10 Nov 2007, 00:04
bmwhype2 wrote:
a rectangular floor measures 2 by 3 meters.
there are 5 white, 5 black and 5 yellow parquet blocks available.
Each block measures 1*1 meter.
In how many different color patterns can the floor be parqueted?

Can someone please tell me why we cannot approach this problem as follows:
We have a total of 15 tiles. We need 6 to fill the floor. The way we can choose 6 tiles out of 15 is 15C6 = 5005.

What is wrong with this logic? I'm assuming that this approach does not account for color combinations? If so, how can we tweak this approach to solve the problem?

I'm pathetic w/ perms & combs so thanks for your help.
Re: Area   [#permalink] 10 Nov 2007, 00:04
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