Find the total number of quadrilaterals when 8 parallel lines intersect another set of 15 parallel lines.

Options

A. 3636
B. 2940
C. 1990
D. 3654

Answer

To find the total number of quadrilaterals formed by the intersection of 8 parallel lines with another set of 15 parallel lines, we can use the combinatorial formula for selecting lines.

### Step-by-step Solution:

1. **Understanding the Problem**:
We have two sets of parallel lines: one set consists of 8 parallel lines (let's call this set M) and another set consists of 15 parallel lines (let's call this set N). A quadrilateral can be formed by selecting 2 lines from set M and 2 lines from set N.

2. **Choosing Lines**:
- From the 8 parallel lines (set M), we need to choose 2 lines. The number of ways to choose 2 lines from 8 is given by the combination formula \( \binom{m}{2} \), where \( m \) is the total number of lines in set M.
- From the 15 parallel lines (set N), we also need to choose 2 lines. The number of ways to choose 2 lines from 15 is given by \( \binom{n}{2} \), where \( n \) is the total number of lines in set N.

3. **Calculating Combinations**:
- For set M (8 lines):
\[ \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28 \]
- For set N (15 lines):
\[ \binom{15}{2} = \frac{15 \times 14}{2 \times 1} = 105 \]

4. **Total Quadrilaterals**:
The total number of quadrilaterals formed is the product of the combinations from both sets:
\[ \text{Total Quadrilaterals} = \binom{8}{2} \times \binom{15}{2} = 28 \times 105 \]

5. **Final Calculation**:
\[ 28 \times 105 = 2940 \]

### Conclusion:
The total number of quadrilaterals formed by the intersection of 8 parallel lines with 15 parallel lines is **2940**.