How many parallelograms will be formed if 9 parallel horizontal lines intersect 8 parallel vertical lines?

To find the number of parallelograms formed by the intersection of parallel lines, we use the formula:

nC2 * mC2

where nC2 is the number of combinations of n items taken 2 at a time (in this case, the horizontal lines), and mC2 is the number of combinations of m items taken 2 at a time (in this case, the vertical lines).

Step 1: Calculate nC2 We have 9 horizontal lines, so nC2 = 9C2 = 36.

Step 2: Calculate mC2 We have 8 vertical lines, so mC2 = 8C2 = 28.

Step 3: Multiply the results Finally, we multiply these two results together to find the total number of parallelograms:

36 * 28 = 1008

So, 1008 parallelograms will be formed if 9 parallel horizontal lines intersect 8 parallel vertical lines.