MAA-BIH ORG

if we imagine there …
if we imagine there to be n points, it is obvious if we were to connect each point to each other point that there is only n-1 possible lines. For n points, each point will have n-1 lines going through it, and because every line has two points on it, there will be (n/2)*(n-1) lines possible for n points, for n=6 this equals 15.

As a i said to the …
As a i said to the professor, i understood bad the problem … maybe because i’m not english hehehe. What i’ve understood was the following: on the plane there were 6 points, and three of them were aligned on the same line so these three points counts only as one line (this is the reason why i substracted 3C2 and added 1 to the 6C2) …

Anyways sorry about the confussion :-/

Although …
Although combinatorics is really just counting things, I think I find it one of the trickiest and potentially confusing areas of all math. I’m curious about the idea behind subtracting 3C2 and adding 1 - looks like an inclusion exclusion method..? Is there a related question to which this is the correct answer?

The solution is 13. …
The solution is 13.

(6 C 2) - (3 C 2) + 1 = 13