Permutation or Combination?

[Zelda22]

Imagine that you have five points in the plane, no three of them in a straight line.

a. Imagine drawing a straight line segment between each pair of points. How many lines would you get?
(Hint: each line segment will be drawn between a pair of points. How many pairs of points can you make from a set of five points?)

Answer: 20

b. Now suppose there are not five but twelve points in the plane, no three of them in a straight line. How many lines would you get?

Answer: 132

I'm confused if I should use Permutation or Combination. Please help. Thanks.

Permutation
a: 20
b: 132

Combination.
a: 10
b: 66

 

[AvgStudent]

Imagine that you have five points in the plane, no three of them in a straight line.

a. Imagine drawing a straight line segment between each pair of points. How many lines would you get?
(Hint: each line segment will be drawn between a pair of points. How many pairs of points can you make from a set of five points?)

Answer: 20

b. Now suppose there are not five but twelve points in the plane, no three of them in a straight line. How many lines would you get?

Answer: 132

I'm confused if I should use Permutation or Combination. Please help. Thanks.

Permutation
a: 20
b: 132

Combination.
a: 10
b: 66

Hi Zelda,
Does it matter if you draw a line from Point A to Point B or from Point B to Point A? Then, you can conclude whether the order matters. If not, then it's combination. If it does, then it's permuatation.
Hope this helps

 

[Zelda22]

Hi Zelda,
Does it matter if you draw a line from Point A to Point B or from Point B to Point A? Then, you can conclude whether the order matters. If not, then it's combination. If it does, then it's permuatation.
Hope this helps

Thank you, I think is a combination. The line between point A and Point B is the same line from B to A.
Combination.
a: 10
b: 66

 

[pka]

Hi Zelda,
Does it matter if you draw a line from Point A to Point B or from Point B to Point A? Then, you can conclude whether the order matters. If not, then it's combination. If it does, then it's permuatation.
Hope this helps

@AvgStudent, two points one distinct line in a plane. Given a plane [imath]\Pi[/imath] in which [imath]A~\&~B[/imath] are two points
then [imath]\overleftrightarrow {AB} = \overleftrightarrow {BA}\ [/imath] is a unique line.
If in the plane [imath]\Pi[/imath] there is a set of [imath]n \ge 2[/imath] points (no three so which are colinear),
then that sets determines [imath]\dbinom{n}{2}=\dfrac{n(n-1)}{2}[/imath] lines.


[imath][/imath][imath][/imath][imath][/imath]

 

[R.M.]

One thing I teach my students is to ask this question: if the order is changed, did something different happen? In your example, changing the order of points did not create a different line. If the question involved rays or vectors, now you have a permutation because ray AB is not the same as ray BA.