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A set of 6 parallel lines is crossed by another set of 5 parallel lines, as in the figure. How many parallelograms are formed?

Competition practicePermutations & Combinations

A30
B300
C165
D150

Step-by-Step Solution

A parallelogram needs 2 lines from each set:

^{6} C_{2} \times^{5} C_{2} = 15 \times 10 = 150. (30 = 6 \times 5

counts crossing points.)

Answer: D) 150

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