Another counting question

[bia]

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 color patterns can be floor be parqueted?
A . 104
B . 213
C . 577
D . 705
E . 726

[kbm1975]

I will attach the file

[Stuart@KaplanGMAT]

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 color patterns can be floor be parqueted?
A . 104
B . 213
C . 577
D . 705
E . 726

Tricksy question!

However, there's a simple solution. 3*2 means we have 6 different blocks. There are 3 possible colours for each block.

If we had an infinite number of each colour, the answer would be 3^6 (i.e. 3*3*3*3*3*3) = 729.

BUT (and here's the tricksy part), we only have 5 of each colour. Among the 729 patters, one is 6 red, one is 6 black and one is 6 white. Since all 3 of those are impossible, the actual number of permutations is:

729 - 3 = 726. Choose (e).

It was surprisingly kind of the question maker not to include 729 among the choices.