There are 10 points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?

Options

A. 90
B. 45
C. 40
D. 30

Answer

To find the total number of straight lines that can be formed by joining 10 points in a plane, where no three points are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have 10 points in a plane, and we need to determine how many straight lines can be formed by joining these points. Since no three points are collinear, any two points will form a unique line.

2. **Choosing Points to Form Lines**:
A straight line is determined by any two points. Therefore, the problem reduces to finding how many ways we can choose 2 points from the 10 points.

3. **Using Combinations**:
The number of ways to choose 2 points from 10 can be calculated using the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 10 \) and \( r = 2 \).

4. **Calculating \( \binom{10}{2} \)**:
\[ \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2! \cdot 8!} \]
Simplifying this, we can cancel \( 8! \) from the numerator and the denominator:
\[ = \frac{10 \times 9 \times 8!}{2 \times 1 \times 8!} = \frac{10 \times 9}{2 \times 1} \]

5. **Final Calculation**:
\[ = \frac{90}{2} = 45 \]

6. **Conclusion**:
Therefore, the total number of straight lines that can be formed by joining the 10 points is **45**.

### Final Answer:
The total number of straight lines that can be formed is **45**.