Solution:

Given: A set of four parallel lines intersecting another set of three parallel lines.

To find: The number of parallelograms that can be formed.

Approach:

- Identify the number of ways to choose two lines from each set.
- Identify the number of ways to choose two lines from these four chosen lines.
- Find the number of parallelograms that can be formed using these four chosen lines.

Calculation:

- We can choose two lines from the set of four parallel lines in 4C2 ways = 6 ways.
- We can choose two lines from the set of three parallel lines in 3C2 ways = 3 ways.
- We can choose two lines from these four chosen lines in 4C2 ways = 6 ways.

Now, we need to find the number of parallelograms that can be formed using these four chosen lines.

- If the two lines from one set are parallel to each other, the other two lines must also be parallel to each other. In this case, only one parallelogram can be formed.
- If the two lines from one set are not parallel to each other, then there are two possible orientations for the other two lines. In each orientation, only one parallelogram can be formed. So, a total of two parallelograms can be formed in this case.

Therefore, the total number of parallelograms that can be formed = 6 x 3 x 2 = 36.

Answer: The correct option is (b) 18.

In order to form a parallelogram, two sets of parallel lines i.e. four linesare required. out of the first set of parallel lines, one set i.e. 2 lines can be selected in 4C2 ways.Similarly from 3 sets of parallel lines, one set can be selected in 3C2 ways.
Number of ways of forming parallelogram
= 4C2 × 3C2
= (4 ×3/2 ×1)× (3×2/2×1)
= (12/2) × (6/2)
= 6× 3
=18 (c)