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

Options

A. 20
B. 60
C. 101
D. 126

Answer

To solve the problem of finding 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 5 parallel lines in one direction and 4 parallel lines in another direction. The intersection of these lines will form parallelograms.

2. **Using the Formula**:
The number of parallelograms formed by \( m \) parallel lines intersected by \( n \) parallel lines can be calculated using the formula:
\[ \text{Number of Parallelograms} = \binom{m}{2} \times \binom{n}{2} \]
where \( \binom{m}{2} \) is the number of ways to choose 2 lines from \( m \) lines, and \( \binom{n}{2} \) is the number of ways to choose 2 lines from \( n \) lines.

3. **Substituting Values**:
Here, \( m = 5 \) and \( n = 4 \).
\[ \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]
\[ \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \]

4. **Calculating the Total Number of Parallelograms**:
Now, we multiply the two results:
\[ \text{Number of Parallelograms} = 10 \times 6 = 60 \]

5. **Final Answer**:
Therefore, the total number of parallelograms formed by the intersection of 5 parallel lines and 4 parallel lines is **60**.