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Bloack measures!!!

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by Ozlemg » Fri Jul 01, 2011 5:41 am
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?
A. 104
B. 213
C. 577
D. 705
E. 726

I dont understand the logic behing when to use which formula? n^r or rCn?

I am confused!
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by Frankenstein » Fri Jul 01, 2011 5:48 am
Hi,
Each of the 6 blocks can be colored with one of the 3 colors right?
So, each block has 3 choices.
So, 6 blocks have 3^6 choices.
But, in this we are considering all six blocks to be of the same color as well, which is not possible because we can have only a maximum of 5 blocks with same colors
all 6 blocks with same color can be in 3 ways - all white, all black, all red.
So, we subtract those 3 cases.
So, 3^6 - 3 = 729-3 =726.

Hence, E
Cheers!

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