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### Lines determined by 5 points

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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?
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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
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
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Associated Topics:
High School Discrete Mathematics

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