# 8-by-8-ft-Area, Two Defective Tiles

• Sep 28th 2006, 01:43 PM
ceasar_19134
8-by-8-ft-Area, Two Defective Tiles
An 8-by-8-ft. area has been tiled with square tiles. Two of the tiles are defective. What is the probabality that the two defective tiles share an edge?

This one I also have absolutly no clue how to do without spending an incredible amount of time on it.
• Sep 28th 2006, 03:00 PM
MathGuru
Take a look at the images,

There are 3 possible 1st tile situations which can be rotated to account for every possible first tile situation, the middle one is twice as probable of happening as the first and 3rd.

Then depending on where the first tile is there are probabilities that the second tile shares an edge with the first.

Quote:

Originally Posted by ceasar_19134
An 8-by-8-ft. area has been tiled with square tiles. Two of the tiles are defective. What is the probabality that the two defective tiles share an edge?

This one I also have absolutly no clue how to do without spending an incredible amount of time on.

• Sep 28th 2006, 03:45 PM
Plato
I have somewhat of a different take on this problem.
Given that we have a room that is oriented.
Therefore we have eight columns and eight rows of eight squares.
There are seven ways for two particular tiles to share an edge in any column or row.
So there are 8*7*2=112 ways for two particular tiles to share an edge.