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IMO E

a parallelogram can be formed by 2 pairs of parallel lines that would intersect to form the two pairs of parallel sides of the parallelogram
therefore we need to select 2 lines from the set of 10 parallel lines = 10C2
and the other two lines from the set of 9 parallel lines = 9C2

=> total possible combinations = 10C2 * 9C2 = 1620
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Bunuel
If ten parallel lines were intersected by another nine parallel lines, then how many parallelograms are formed?

A. 72
B. 1008
C. 1320
D. 1520
E. 1620

We need any two lines from the set of ten. We have 10 choices for the first and 9 for the second. 10*9 = 90. AB is the same as BA, so we need to divide by 2. 90/2 = 45.

We need two lines from the set of nine. We have 9 choices for the first and 8 for the second. 9*8 = 72. AB is the same as BA, so we need to divide by 2. 72/2 = 36.

36*45 = 1620

Answer choice E.
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