Algebra, lines intersection?

Question

n parallels lines between themselves are set among m parallels lines between themselves but not with the n lines.
a) How many points are made with the intersections of the lines? (Drawing the situation, I think it's easy to see that it's n.m)
b) How many parallelograms are determinated by the intersections of the lines? (Couldn't do it).
Please tell me if I was right for a), and please explain me the answer of part b. Thanks a lot.

Answer 1

a) Each of the n parallel lines in the first set intersect with each of the m parallel lines in the second set for a total of mn intersections.

b) You have an m by n grid. You have parallelograms of various sizes. The number of each size is:
1 by 1 = (m - 1)(n - 1)
1 by 2 = (m - 2)(n - 1)
1 by 3 = (m - 3)(n - 1)
...
1 by (m - 1) = 1(n - 1) = n - 1

Then look at:
2 by 1 = (m - 1)(n - 2)
2 by 2 = (m - 2)(n - 2)
2 by 3 = (m - 3)(n - 2)
...
2 by (m - 1) = 1(n - 2) = n - 2

Continue until you get
(m - 1) by (n - 1) = 1*1 = 1

Then sum them up.