How many distinct lines can be formed by connecting 2 of these points?

Question

If there are 8 points in a plane, no 3 of which are collinear, how many distinct lines can be formed by connecting 2 of these points?

Answer 1

Label the points 1-8

Connecting any 2 distinct points

will create a line.

 

Pairs with point 1... 7

Pairs with point 2... 6

Pairs with point 3... 5

Pairs with point 4... 4

Pairs with point 5... 3

Pairs with point 6... 2

Pairs with point 7... 1

Pairs with point 8... 0

                        ---------

                        28 lines

The above pairs decrease each time because

the line through points 1,2 is the same as the

line through points 2,1 and so forth