Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that that can be formed joining the point.

Answer

To solve the problem of finding the number of lines that can be formed by joining 18 points in a plane, where no three points are collinear except for five points that are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Points**:
- We have a total of 18 points.
- Out of these, 5 points are collinear (let's call them A1, A2, A3, A4, A5).
- The remaining 13 points (let's call them B1, B2, ..., B13) are not collinear with each other or with the collinear points.

2. **Counting Lines from Non-Collinear Points**:
- To form a line, we need to select 2 points.
- The number of lines that can be formed from the 13 non-collinear 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.
- Therefore, the number of lines from the 13 points is:
\[ \text{Lines from 13 points} = \binom{13}{2} = \frac{13 \times 12}{2} = 78 \]

3. **Counting Lines Involving Collinear Points**:
- The 5 collinear points can only form one line as they are all on the same line.
- Thus, the contribution from the 5 collinear points is:
\[ \text{Lines from 5 collinear points} = 1 \]

4. **Counting Lines Between Collinear and Non-Collinear Points**:
- Each of the 5 collinear points can form a line with each of the 13 non-collinear points.
- Therefore, the number of lines formed between the collinear points and the non-collinear points is:
\[ \text{Lines between collinear and non-collinear points} = 5 \times 13 = 65 \]

5. **Total Number of Lines**:
- Now, we can sum all the lines calculated:
\[ \text{Total lines} = \text{Lines from 13 points} + \text{Lines from 5 collinear points} + \text{Lines between collinear and non-collinear points} \]
\[ \text{Total lines} = 78 + 1 + 65 = 144 \]

### Final Answer:
The total number of lines that can be formed by joining the points is **144**.