Find the number of straight lines formed by joining 6 different points on a plane, no three of them being collinear.

Options

A. 21
B. 15
C. 16
D. 24

Answer

To find the number of straight lines formed by joining 6 different points on a plane, where no three points are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine how many straight lines can be formed by joining pairs of points from a set of 6 distinct points.

2. **Identifying the Requirement**:
A straight line is formed by joining any two points. Therefore, to find the total number of straight lines, we need to find the number of ways to choose 2 points from the 6 points.

3. **Using Combinations**:
The number of ways to choose 2 points from 6 can be calculated using the combination formula:
\[ nCk = \frac{n!}{k!(n-k)!} \]
Here, \( n = 6 \) (the total number of points) and \( k = 2 \) (the number of points needed to form a line).

4. **Calculating the Combinations**:
\[ 6C2 = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \cdot 4!} \]
Simplifying this:
\[ 6C2 = \frac{6 \times 5}{2 \times 1} = \frac{30}{2} = 15 \]

5. **Conclusion**:
Therefore, the total number of straight lines that can be formed by joining the 6 different points is **15**.