# Number of possible combinations of...

#### Rosebud

How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct point?

#### phinds

Gold Member
How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct point?
In 3D coordinates, how many "quadrants" are there?

#### Rosebud

EDIT: OK, I understand now. Thank you.

Last edited:

#### phinds

Gold Member
Right. So how many ways could you have the point positioned, from the point of view of differing signs?

#### HallsofIvy

Homework Helper
As the names imply, in two dimensions there are four "quadrants" and in three dimensions there are eight "octants. In n dimensions there are $2^n$ such subsets.

#### phinds

Gold Member
Yeah, that's why I put "quadrants" in quotes, to mean just "sections", which you more appropriately identified as octants.

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