There 12 points in a plane of which 5 are collinear . Find
the number of straight lines obtained by joining these points in pairs.

Answer

To solve the problem of finding the number of straight lines obtained by joining 12 points in pairs, where 5 of these points are collinear, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Total Points**: We have a total of 12 points in a plane.

2. **Calculating Lines Without Considering Collinearity**: If all 12 points were non-collinear, the number of lines that can be formed by joining these points in pairs can be calculated using the combination formula:
\[ \text{Number of lines} = \binom{12}{2} \]
This is because a line is determined by any two points.

3. **Calculating the Total Combinations**:
\[ \binom{12}{2} = \frac{12 \times 11}{2 \times 1} = 66 \]

4. **Considering the Collinear Points**: Since 5 of these points are collinear, they do not form distinct lines when paired together. Instead, they form only one line.

5. **Calculating the Lines Among Collinear Points**: The number of lines that can be formed by the 5 collinear points is:
\[ \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]
However, since these 5 points are collinear, they only contribute 1 line instead of 10.

6. **Adjusting the Total Lines Count**: To find the actual number of distinct lines, we need to subtract the 10 lines (which we counted) and add back 1 line (the actual line formed by the 5 collinear points):
\[ \text{Total distinct lines} = \binom{12}{2} - \binom{5}{2} + 1 = 66 - 10 + 1 = 57 \]

7. **Final Answer**: Therefore, the total number of distinct straight lines that can be formed by joining these points in pairs is:
\[ \text{Number of distinct lines} = 57 \]

### Summary:
The total number of straight lines obtained by joining the 12 points in pairs, considering that 5 of them are collinear, is **57**.