Maximum number of points of intersection of 6 straight lines is :

Options

A. 30
B. 15
C. 28
D. none of these

Answer

To find the maximum number of points of intersection of 6 straight lines, we can use the concept of combinations. The maximum number of intersection points occurs when no two lines are parallel and no three lines are concurrent (i.e., they do not meet at a single point).

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the maximum number of intersection points formed by 6 straight lines. Each pair of lines can intersect at one point.

2. **Using Combinations**: The number of ways to choose 2 lines from 6 lines is given by the combination formula \( nCk \), where \( n \) is the total number of lines and \( k \) is the number of lines we are choosing. In this case, \( n = 6 \) and \( k = 2 \).

\[ \text{Number of intersection points} = 6C2 \]

3. **Calculating \( 6C2 \)**: The formula for combinations is:

\[ nCk = \frac{n!}{k!(n-k)!} \]

For \( 6C2 \):

\[ 6C2 = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \cdot 4!} \]

We can simplify this:

\[ 6C2 = \frac{6 \times 5}{2 \times 1} = \frac{30}{2} = 15 \]

4. **Conclusion**: Therefore, the maximum number of points of intersection of 6 straight lines is \( 15 \).

### Final Answer:
The maximum number of points of intersection of 6 straight lines is **15**.

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