Combinations and a bit of probability
Another set of interesting questions:
1. In how many ways can four squares, not all in the same row or column be selected from an 8-by-8 chessboard to form a rectangle?
2. A gardener plants three maple trees, four oak trees and five birch trees in a row. He plants them in random order, each arrangement being equally likely. Find the probability that no two birch trees are next to one another.
3. 25 people sit around a circular table. Three of them are chosen randomly. What is the probability that at least two of the three are sitting next to one another?