Given four 6 collinear points, make a conjecture about the number of ways to connect different pairs of points

The correct answer is: 15 ways to connect different pairs of points

We have given the 6 collinear points
We have to find the number of ways to connect the different pairs of points
We will consider figure of the line

We will consider the points from A to F
Here we will consider point A
Point A have 5 options to pair, that are B, C, D, E, F.
If we consider point B then,
Point B have 4 points to pair that are C, D , E, F . Because we have considered the pair with A before.
If we consider point C then,
Point C have 3 points to pair , that are D, E, F .
If we consider point D then
Point D have 2 points to pair , that are E, F.
If we consider point E then
Point E have 1 point to pair, that is F
Therefore total number of ways the points can be paired is = 5 + 4 + 3 + 2 + 1= 15
There are 15 ways to connect different pairs of points.