Problem Solving

A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black and 5 red parquet block available. If each block measure 1 by 1 m, in how many different color patterns can the floor be parqueted?

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

floor=2*3 meters and thus it means 6 tiles can be placed
for 1st tile, we have 3 options
for 2nd, we have 3 options
3rd-3
4th-3
5th-3
6th-3
Total=3*3*3*3*3*3 = 729
cases when for all of 6 we choose the same color = 3 (all white, all black and all red)
Thus subtract these (as we only have 5 tiles of each color)
729-3 = 726
IMO E

3^6 - 3 = 726

E

There are only 5 blocks of each color available, hence you cannot cover the entire floor with one color. We have to subtract three patterns that have only one color.

IMO E