How many straight lines can be drawn from 15 non-collinear points?

Options

A. 105
B. 120
C. 110
D. 115

Answer

To find the number of straight lines that can be drawn from 15 non-collinear points, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We need to determine how many straight lines can be formed using 15 non-collinear points.
- A straight line is defined by two distinct points.

2. **Choosing Points**:
- Since we can form a line by selecting any two points, we need to calculate the number of ways to choose 2 points from the 15 available points.

3. **Using Combinations**:
- The number of ways to choose 2 points from 15 can be calculated using the combination formula:
\[ nCr = \frac{n!}{r!(n-r)!} \]
- Here, \( n = 15 \) (the total number of points) and \( r = 2 \) (the number of points to choose).

4. **Calculating 15C2**:
- Plugging in the values:
\[ 15C2 = \frac{15!}{2!(15-2)!} = \frac{15!}{2! \cdot 13!} \]
- This simplifies to:
\[ 15C2 = \frac{15 \times 14}{2 \times 1} = \frac{210}{2} = 105 \]

5. **Conclusion**:
- Therefore, the total number of straight lines that can be drawn from 15 non-collinear points is **105**.

### Final Answer:
The number of straight lines that can be drawn from 15 non-collinear points is **105**.

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