What Is the Fundamental Counting Principle?

Dirock has a very neat rectangular backyard that can be represented as a $32\times 32$ grid of unit squares. The rows and columns are each numbered $1,2,\ldots, 32$. Dirock is very fond of rocks, and places a rock in every grid square whose row and column number are both divisible by $3$. Dirock would like to build a rectangular fence with vertices at the centers of grid squares and sides parallel to the sides of the yard such that

• The fence does not pass through any grid squares containing rocks;
• The interior of the fence contains exactly 5 rocks.

In how many ways can this be done?

Source: 2012-2013 Winter Online Math Open