Question

# 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.

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.