Math Is Fun Forum

cncnorman

Member

Registered: 2008-07-18

Posts: 2

How to name a plane

My professor gave up this problem:
Points A, B, C, D, and E are all coplanar and no three are colinear.  In how many ways can the plane be named using only these points?  Assume that different order means different names. 

The only thing the textbook tells me is that a plane is named by the points on it.  It does not discuss different ways to name a plane and I am confused.

Christina

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: How to name a plane

One point gives you ... well... a dot.
Two points gives you a line.
Three point gives you a plane.

You use the points to name the plane, like you would name a triangle Triangle ABC, you name a plane Plane ABC.

So you could have: ABC, ACB, DCA, EDC, BCD, DCB etcetcetcetcetcetcetc.

I think this is a counting problem, you need to find how many ways you can arrange 5 objects (ABCDE) into 3 positions.
I am not sure if ABC and ACB count as the same way of naming plane, but I am assuming that they don't.

So the answer is

ways.

cncnorman

Member

Registered: 2008-07-18

Posts: 2

Re: How to name a plane

Thank you so very much.  So, if order makes a difference this is a permutation problem?  I tried to figure it out using nPr to get the answer and came up with the same thing you go.  I am grateful for your assistance.
Christina