Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.

The correct answer is: 4 + 3 + 2 + 1 = 10

We have given the 5 non-collinear points
We have to find the number of ways to connect the different pairs of points
We will consider figure

We will consider the points from A to E
Here we will consider point A
Point A have 4 options to pair, that are B, C, D, E.
If we consider point B then,
Point B have 3 points to pair that are C, D , E. Because we have considered the pair with A before.
If we consider point C then,
Point C have 2 points to pair, that are D, E.
If we consider point D then
Point D have 1 point to pair, that are E.
Therefore total number of ways the points can be paired is = 4 + 3 + 2 + 1 = 10