# Permutations .How do u find the number of paths in a 3D object?

• gillgill
In summary, the conversation discussed the number of paths in a 3D object, specifically a cube, from point A to point B. It was mentioned that the formula for finding the distance in 3D is the same as in 2D, with an extra variable representing the third dimension. The conversation also touched on drawing a 3D object in 2D and counting the number of paths between two points, using a lattice coordinate plane. A 2D representation of a cube was provided as an example.

#### gillgill

Permutations...
How do u find the number of paths in a 3D object?...let say a cube...from A to B...

I don't understand?

maby you want the distance from A to B in 3D? Its the same formula as in 2D just an extra variable
squareroot(x^2 + y^2 + z^2)

assuming B is relative to A and those are B's cooridinates to A.

Hope this helps!

gillgill,
It doesn't matter whether the object is 3D or 2D. What does matter is how many nodes and how are their interconnections. You can draw a 3D cube in a 2D way and calculate the number of paths from A to B without affecting anything. (All u have to make sure that u are representing every edge of 3D object in 2D diagram)

-- AI

how do u know how to draw it in 2D?...and from which point to which point?

I'm also not sure where you're going with all of this. There's an infinite amount of paths between any two points in R^3, same thing with R^2. If you're talking about like, a lattice coordinate plane, this is different. A lattice coordinate plane only has "points" at integers, so it's actually feasible to count the number of paths between two points in a cube that is set in the lattice plane. If this is what you want (or if it isn't), please clarify.

...*--------*
../|... /|
./.|.../.|
*--------*..|
|..|...|..|
|..*------|--*
|./...|./
|/...|/
*--------*

Above i represent a cube in 2D (albeit in a very shabby way), but u would see that i have done 2D representation of the 3D cube and each node of the cube and each edge of the cube can be uniquely mapped to this figure.

-- AI

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## 1. What is a permutation?

A permutation is an arrangement of objects or events in a specific order. It is a mathematical concept used to determine the number of ways that a set of objects can be ordered or arranged.

## 2. How do you calculate the number of permutations?

The number of permutations can be calculated by using the formula n! / (n-r)! where n is the total number of objects and r is the number of objects being arranged or selected.

## 3. Can you give an example of a permutation?

Let's say you have 4 different colored pencils and you want to arrange them in a specific order. The number of permutations for this scenario would be 4! = 24. The 24 possible arrangements would be: red, blue, green, yellow; red, blue, yellow, green; red, green, blue, yellow; and so on.

## 4. How are permutations different from combinations?

Permutations and combinations are both ways of counting objects, but they have different rules and calculations. Permutations take into account the order of objects, while combinations do not. Additionally, in permutations, repetition is not allowed while in combinations it is.

## 5. How do you find the number of paths in a 3D object?

The number of paths in a 3D object can be found by calculating the number of permutations for each direction (x, y, z). For example, if you have a cube with 3 layers, there would be 3! = 6 possible paths in the x-direction, 3! = 6 possible paths in the y-direction, and 3! = 6 possible paths in the z-direction. Then, you can multiply these numbers to find the total number of paths, which would be 6 x 6 x 6 = 216 paths.