If there are six straight lines in a plane, no two of which are parallel and no three of which pass through the same point, then find the number of points in which these lines intersect.

Explanation

To find the number of points in which six straight lines intersect in a plane, where no two lines are parallel and no three lines meet at the same point, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem:**
We have 6 lines in a plane. The conditions state that no two lines are parallel, meaning each pair of lines will intersect at a unique point. Additionally, no three lines intersect at the same point, ensuring that each intersection point is distinct.

2. **Counting Intersections:**
To determine the number of intersection points formed by the lines, we can use the concept of combinations. The number of ways to choose 2 lines from 6 lines can be calculated using the combination formula:
\[ \text{Number of intersection points} = \binom{n}{2} \]
where \( n \) is the total number of lines.

3. **Calculating Combinations:**
Here, \( n = 6 \). Thus, we need to calculate \( \binom{6}{2} \):
\[ \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \]

4. **Conclusion:**
Therefore, the total number of points in which these 6 lines intersect is 15.

### Final Answer:
The number of points in which the six lines intersect is **15**.

---