Counting the number of lines through a given set of points, some of which are collinear What does counting total number of lines mean? What type of lines does it include? 
Especially I'm very confused about collinear points. Like in this example,  below. 

Consider $10$ points on a plane out, of which $4$ are collinear. Find the total number of lines that can be drawn through those points.

(Actually everywhere) they say that lines are $ \space C(10,2)-C(4,2)+1$.
I can understand why $C(10,2)$ is done, but why $C(4,2)$ and $-1$. 
Everywhere they say that $C({4,2})$ are lines made by collinear points so we have to subtract them and the we add $1$ because we have also subtracted the mainline. 
What does all this mean?? Please explain with a physical context and simple to understand language.
 A: Because as there are $4$ points collinear, then in the $4$ points that are collinear, we can choose two points, then there are $C^4_2$ ways to make lines from the four points. But the $C^4_2$ lines are the same! So we have to subtract $C^4_2$. But there is a problem again! We subtracted all the lines joining the four collinear points! As every line has to be counted once, but this is not, we have to add $1$. Hope this helps!
A: There are $\binom{10}{2}$ ways to select a pair of points.
In the event that no three or more of the points all lied on the same line, then all $\binom{10}{2}$ of these would have resulted in distinct lines.  That is not the case for us however.  We are told that four of our points are colinear.
We want to count that line that the four colinear points lie on exactly once, but we had accidentally counted it $\binom{4}{2}$ times in the above.  So, to correct our count, we can subtract $(\binom{4}{2}-1)$ from the total to remove the number of times that we counted it too much leaving us as having counted that line exactly once as desired.
