Four horizontal lines and four vertical lines are drawn in a plane. In how many ways can four lines be chosen such that a rectangular region is enclosed?
To form a rectangular region, I need to choose two horizontal lines and two vertical lines. There are four horizontal lines, so I can choose any two of them in 4 choose 2 ways, which is 4 times 3 over 2, or 6 ways. Similarly, there are six ways to choose two vertical lines. For each pair of horizontal lines, I can pair them with any pair of vertical lines, so I can multiply the number of ways. Therefore, the total number of ways to choose four lines that form a rectangle is 6 times 6, which is 36. 