A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors r patterns can be floor be parqueted? Choose the correct option.
A) 104
B) 213
C) 3^5
D) 705
E) 726
Total number of squares we need to fill = 6   Number of colors we have r= 3   Therefore, total number of patterns = 3*3*3*3*3*3= 
<gadget id="calculator">3*3*3*3*3*3</gadget>
<output>729</output>
729   However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).   Thus our answer should be :729 - 3= 
<gadget id="calculator">729 - 3</gadget>
<output>726</output>
726   Answer : 726
<result>E</result>
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors r patterns can be floor be parqueted?