Question

How many different lines pass through a 3x3-point grid if a line only needs two points?

Answer 1

Well, there are 9 points. If you choose 2 of them, that gives a straight line. So you can try to find all the ways you can choose two points.

But you over-count, because some lines go through three points. So the question is 1: How many lines go through 3 points? And 2: How many times have you 'over-counted' these lines?

Explanation:

Answer 2

How many different lines pass through a 3x3-point grid if a line only needs two points?

Explanation:

The answer being (93)=9! 3! 6! =9⋅8⋅73⋅2⋅1=84 possible arrangements.