How Many Basic States Exist for Particles in Divided Spaces?

[Galactium]

Homework Statement

Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located.

1. How many basic states are there?
2. The door to this room is opened, allowing the particles to move into an adjacent, identical room, also divided into octants. Now that the amount of space that can be occupied has been doubled, by what factor has the number of basic states increased?

Homework Equations

Ω=M^N ?[/B]

The Attempt at a Solution

Honestly, I do not even know how to start this problem. I have read the Mazur chapter 19 Entropy, but I still do not quite understand it.

 

[Orodruin]

So let us start by understading the question. What would you say that a basic state is?

 

[Galactium]

So let us start by understading the question. What would you say that a basic state is?

A basic state, also know as Microstate, is amount of distinguishable particles in a system. Whereas the Macrostate is in a larger scale in describing it by its properties, volume, pressure, temperature, etc.

 

[Orodruin]

A basic state, also know as Microstate, is amount of distinguishable particles in a system

No, this is not correct. A basic state is a possible configuration that completely describes all the particles in the system.