Average number of particles/subsystems in a state

[devd]

Homework Statement

A system in thermal equilibrium at temperature T consists of a large number

of subsystems, each of which can exist only in two states of energy

and

, where

. In the expressions that follow, k is the Boltzmann constant.

For a system at temperature T, the average number of subsystems in the state of energy

is given by

1. 
2. 
3. 
4. 
5. 

Homework Equations

Probability of a system to be in a system-microstate of total energy ##E_R##,
##P_R = \frac{e^{-\beta E_R}} {\sum_{R} e^{-\beta E_R}} ##

The Attempt at a Solution

We have the constraint ##\sum_r n_r= N_0 ## and ## \sum_r n_r \epsilon_r = E_R##
Where, r labels the single particle states.
Therefore, the average number of particles in the sth 1 particle state,
##\langle n_s\rangle = \frac{\sum_R n_s e^{-\beta (\sum_r n_r \epsilon_r)}}{\sum_{R} e^{-\beta (\sum_r \epsilon_r)}}##

To proceed one needs the nature of the particles.
For example,
## \langle n_s\rangle = \frac{1}{e^{\beta \epsilon_s} -1}## for Photons
## \langle n_s\rangle = \frac{1}{e^{(\beta \epsilon_s -\mu)}+1}## for FD statistics etc.

How do i proceed without further info? The question seems to conflate states of the total system with the subsystem states. I think the question is problematic and ambiguous. Anyhow, the supplied 'correct' answer is option (B).

 

[devd]

The given options only makes sense if by 'system' they mean ensemble and by 'subsystem' they mean members of the ensemble.
Then, ##P(E_1)= \cfrac{e^{-\beta E_1}}{e^{-\beta E_1}+e^{-\beta E_2}}##
Again, ##P(E_1)= \cfrac{N_1}{N_0}. ## Therefore, ##N_1 = N_0\left(\cfrac{e^{-\beta E_1}}{e^{-\beta E_1}+e^{-\beta E_2}}\right)##
And hence, ##N_1 = N_0\left(\cfrac{1}{1+e^{-\beta \epsilon}}\right)## , where ## E_2-E_1= \epsilon## .

But, if they're talking about a single system, then the options don't make sense to me. But, this question appeared in the GRE, so they aren't likely to make such errors. So, what am i missing?