# States counting of many particales under a constraint

1. Oct 27, 2009

### oneshai

Let’s say i have n identical classical non interacting particles and N sites where i can put them in. BUT the total energy is given.
The number of possible states is (N)^n/n!/(n/2)!
Where N^n is the total possibilities to arrange the particles.
We divide it by n! since they are identical.
and the reason we divide by (n/2)! has some thing to do with the fact that the energy is given but I don’t know how.

i whould be very thankful to any one who can say why (n/2)!

thanks shai

2. Oct 27, 2009

### xepma

What determines the energy for a given distribution? This is kinda the input you need for the question you're asking...

3. Oct 27, 2009

### oneshai

Maxwell - Boltzman as usual. I though about it but i fail to see how it leads to the n/2!

4. Oct 27, 2009

### xepma

No, no, that's a distribution function for finite temperature. You're working in a microcanonical ensemble, so you don't have temperature (the energy is fixed).

What I'm asking is: what's the energy for a given configuration of the particles among the lattice sites. Do all configurations give the same energy or not? It's the only possible source of where the (n/2)! is coming from as far as I can tell.