Number of lines passing through five points such that no three of them are collinear is

Question

Philoid · Accepted Answer

Consider the points named A, B, C, D, and E. such that no three of them are collinear. It can simply be assumed to form a pentagon. Now draw the diagonals in the figure and count the total number of lines including sides of pentagon.

So the lines are AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.

So that makes 10 lines.

Now, let’s start counting lines.

AB, AC, AD, AE

BC, BE (BD would be same as BC and BA is covered in above in AB)

CE

DE

∴ there are 8 combinations