There are 10 points in a plane out of which 5 are collinear. The number of straight lines than can be drawn by joining these points will be

Options

A. 35
B. 36
C. 45
D. 24

Answer

To solve the problem of finding the number of straight lines that can be drawn by joining 10 points in a plane, where 5 of the points are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have 10 points in total, out of which 5 points are collinear. Collinear points are points that lie on the same straight line.

2. **Calculating Total Lines from 10 Points**:
The total number of lines that can be formed by joining any 2 points from 10 points is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of points and \( r \) is the number of points to choose. Here, \( n = 10 \) and \( r = 2 \):
\[ \text{Total lines} = \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45 \]

3. **Calculating Lines from Collinear Points**:
Since 5 of the points are collinear, they can only form 1 line. The number of lines that can be formed by choosing any 2 points from these 5 collinear points is:
\[ \text{Collinear lines} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]
However, these 10 combinations only form 1 unique line.

4. **Adjusting for Overcounting**:
To find the total number of unique lines, we need to subtract the overcounted lines formed by the collinear points. Therefore, we subtract the 9 extra lines from the total:
\[ \text{Unique lines} = \text{Total lines} - (\text{Collinear lines} - 1) = 45 - (10 - 1) = 45 - 9 = 36 \]

5. **Final Count of Unique Lines**:
Thus, the total number of unique straight lines that can be drawn by joining these points is:
\[ \text{Final Answer} = 36 \]

### Final Answer:
The number of straight lines that can be drawn by joining these points is **36**.