I came across a question that goes as follows:

**Find the number of straight lines if there are 11 points in a plane of which 5 are collinear.**

The following is how I approached the problem:

Since 5 of the 11 points are collinear, 6 points are non-collinear. We can use these 6 points AND one point from those 5 collinear points to make our lines, a total of 7 points.
And from these 7 points, we can choose 2 to make our straight lines in 7C2 ways.

This however is not the right answer. The right answer is 46.

Could someone explain where I am going wrong? Approaches better than this are also welcome!

Thanks!