Q:

$10$ parallel lines are all perpendicular to 10 other parallel lines. How many rectangles are formed?

I guess the answer is $ 100 \choose 4$ since there are $100$ lines in total and $4$ lines form a rectangle. Is that correct?

A:

You need the lines to intersect one another.  If you pick four parallel lines it won't form a rectangle.
Note that you need two lines from the first set of parallel lines, and two lines from the second set.  Thus, you need to consider ${10 \choose 2 }^2$ instead.

