Question 457560: when nine parallel lines, intersect ten parallel lines , how many parallelograms are formed?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Consider an 8x9 rectangle (or parallelogram, but it actually doesn't matter) lying on a grid of lattice points. To choose a parallelogram, we could choose any pair out of the eight horizontal lines, followed by any pair out of the nine vertical lines. This would result in some rectangle (parallelogram if we bent the shape). Hence, the number of parallelograms is
(8C2)*(9C2)
= 28*36 = 1008.
|
|
|
