If 5 parallel straight lines are intersected by 4 parallel straight lines, then find the number of parallelograms thus formed.

Options

A. A) 20
B. B) 40
C. C) 60
D. D) 50

Answer

To find the number of parallelograms formed by 5 parallel straight lines intersected by 4 parallel straight lines, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two sets of lines:
- Set 1: 5 parallel lines (let's call them L1, L2, L3, L4, L5)
- Set 2: 4 parallel lines (let's call them M1, M2, M3, M4)

A parallelogram is formed by selecting 2 lines from Set 1 and 2 lines from Set 2.

2. **Selecting Lines from Set 1**:
To form a parallelogram, we need to choose 2 lines from the 5 lines in Set 1. The number of ways to choose 2 lines from 5 can be calculated using the combination formula:
\[ \text{Number of ways} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 5 \) and \( r = 2 \):
\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

3. **Selecting Lines from Set 2**:
Next, we need to choose 2 lines from the 4 lines in Set 2. Using the same combination formula:
\[ \text{Number of ways} = \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

4. **Calculating Total Parallelograms**:
The total number of parallelograms formed is the product of the number of ways to choose lines from Set 1 and Set 2:
\[ \text{Total parallelograms} = \binom{5}{2} \times \binom{4}{2} = 10 \times 6 = 60 \]

5. **Final Answer**:
Therefore, the total number of parallelograms formed is **60**.