# counting points

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• Nov 13th 2006, 01:10 PM
mdizzle12830
counting points
Given 6 points, no 4 of which are collinear, what is the maximum number of lines that can be represented? What is the minimum number of lines that can be represented? (Keep a graphical representation of this, as I might ask to see your diagram of the situation)

can anyone solve this or at least tell me how to start this equation.

thanks
• Nov 13th 2006, 02:01 PM
ThePerfectHacker
Quote:

Originally Posted by mdizzle12830
Given 6 points, no 4 of which are collinear, what is the maximum number of lines that can be represented? What is the minimum number of lines that can be represented? (Keep a graphical representation of this, as I might ask to see your diagram of the situation)

Tha maximum is when no 3 are collinear. For example, all 6 are lying on a circle. So then the number of lines that can be drawn is the number of ways selecting two points from 6 points that is $_6C_2=15$

The minimum seem like the wrost case scenario. That is ,
Code:

```*    *    *           *           *```
6
• Nov 13th 2006, 03:45 PM
OReilly
Quote:

Originally Posted by ThePerfectHacker
Tha maximum is when no 3 are collinear. For example, all 6 are lying on a circle. So then the number of lines that can be drawn is the number of ways selecting two points from 6 points that is $_6C_2=15$

The minimum seem like the wrost case scenario. That is ,
Code:

```*    *    *           *           *```
6

Your diagram of minimum lines contains only 5 points.

Minimum lines diagram can be:
Code:

```*    *    * *    * *```
Minimum is 9 lines.
• Nov 13th 2006, 05:33 PM
ThePerfectHacker
Quote:

Originally Posted by OReilly
Your diagram of minimum lines contains only 5 points.

Minimum lines diagram can be:

Opps, I started counting from 2.
• Nov 13th 2006, 05:43 PM
mdizzle12830
????????
i didnt really understand what you said, i really don't care how to do it, i just need the answer. thank you very much, i really appreciate it.