Lines determined by 5 points

Date: Sun, 13 Nov 1994 13:34:47 -0500
From: Anonymous
Subject: geometry

Can somebody please answer this question:  How many lines are determined 
by 5 points, no three of which are collinear?

Date: Sun, 13 Nov 1994 16:16:36 -0500 (EST)
From: Dr. Ken
Subject: Re: geometry

Hello there!

You probably already know that two points determine a unique line.  So 
your question can be rephrased as this: "how many different ways can 
we choose two points from a set of five points?"  Since no three of 
these are collinear, you won't end up determining the same line twice 
by choosing different points; i.e. looking at the problem this way will 
give you the right answer.  

If the points we have are A, B, C, D, and E, then here are a few 
examples of lines we could get by choosing two at a time.

AB
AC
AD
AE
BC
BD

and so on.  Do you see any good, ordered way to list all the different 
ways to choose two points from this set of five points?  If you can list 
all such combinations, you'll have names for all the lines, and you can 
just count them up!

I hope this helps.  Write back if you need more help!

-Ken "Dr." Math