# Number of possible combinations of....

• Rosebud
In summary, the conversation discussed finding all the different combinations of a point (x,y,z) when x,y, and z can be positive or negative. It was mentioned that there are eight octants in 3D coordinates and the number of subsets of points increases with each dimension. The concept of "quadrants" was also mentioned but it was clarified that it refers to sections or subsets of points.
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?

Rosebud said:
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?

There are eight octants. I'm not sure about quadrants. EDIT: OK, I understand now. Thank you.

Last edited:
Rosebud said:
Right. So how many ways could you have the point positioned, from the point of view of differing signs?

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.

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

## 1. What is the formula for calculating the number of possible combinations?

The formula for calculating the number of possible combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen or arranged.

## 2. How do I use the formula to find the number of possible combinations?

To use the formula, plug in the values for n and r and then simplify the equation. For example, if you have 10 items and want to find the number of combinations when choosing 3 at a time, the equation would be 10C3 = 10! / (3!(10-3)!) = 120.

## 3. Can the formula be used for any type of combination?

Yes, the formula can be used for any type of combination, whether it is a combination with or without repetition. However, for combinations with repetition, the formula would be n^r instead of nCr.

## 4. How does the number of possible combinations change when the number of items or the number of items being chosen is increased?

The number of possible combinations increases significantly as the number of items or the number of items being chosen is increased. For example, if you have 10 items and are choosing 2 at a time, there are 45 possible combinations. But if you are choosing 5 at a time, there are 252 possible combinations.

## 5. Can the formula for calculating combinations be applied to real-life situations?

Yes, the formula for calculating combinations can be applied to real-life situations, such as in probability and statistics. It can be used to determine the number of outcomes in a game of chance or the number of possible combinations in a lock code.

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