The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of

Question

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

Accepted Answer

To form a parallelogram, we need to select two parallel lines from the first set and two parallel lines from the second set.

1.  Number of ways to choose 2 lines from the first set of 4 parallel lines:
    This is a combination problem, C(n, k) = n! / (k! * (n-k)!).
    C(4, 2) = 4! / (2! * (4-2)!) = (4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1)) = 24 / 4 = 6.

2.  Number of ways to choose 2 lines from the second set of 4 parallel lines:
    Similarly, C(4, 2) = 6.

3.  Total number of parallelograms:
    To find the total number of parallelograms, we multiply the number of ways to choose lines from each set, as any selection from the first set can be combined with any selection from the second set.
    Total parallelograms = (Ways to choose from first set) * (Ways to choose from second set)
    Total parallelograms = 6 * 6 = 36.

Therefore, the correct answer is D) 36.

Answer

18

Answer

24

Answer

32

Answer

36

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

Explanation

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