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General

Easy

Question

# 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

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

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