How many lines in 8 non collinear points?

Answer 1

28

Good question. This is an 'analogue' of this puzzle: "Eight people meet for the first time. If they each shake hands with everyone else, how many handshakes are there?" There is a formula, but who would remember it?

Imagine you and I are both among the eight people. You would shake hands with seven others. I would say the same thing, and so could each of the others.

That gives 8x7 = 56, but you and I both counted the time we shook hands with one another , in fact each handshake is counted twice. The number of handshakes is actually 56/2 = 28.

This can be generalized to say that the number of ways to choose 2 objects from a group of n objects is n(n-1)/2.