There are 10 points on a plane of which no three points are collinear. If lines are formed joining these points, find the maximum points of intersection of these lines.

Explanation

To find the maximum number of points of intersection formed by lines joining 10 points on a plane where no three points are collinear, we can follow these steps:

### Step 1: Determine the number of lines formed
Given that we have 10 points and no three points are collinear, we can form lines by selecting any two points. The number of ways to choose 2 points from 10 is given by the combination formula:

\[ \text{Number of lines} = \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45 \]
...