One of the more esoteric notions in STATISTICAL MECHANICS is the concept of an ensemble. This has nothing to do with music; it goes back to the original meaning of the French word ensemble, which is a collection or gathering of things - much more general and abstract than the small band of musicians we tend to visualize. Anyway, the Statistical Mechanical " ENSEMBLE" is a collection of all the possible fully specified states of some system.
Of course, there are different kinds
of ENSEMBLES depending upon what global constraints
are in effect. For instance, the set of all possible states
of an isolated system 
consisting of a fixed number N of "particles"15.10
with a well defined total energy U is called a
MICROCANONICAL ENSEMBLE.
This is what we have been discussing so far.
The set of all possible states
of a system
consisting of
a fixed number N of particles
but in "thermal contact" with a much, much larger
system 
(called a "heat reservoir")
so that the energy U of
can flow in or out of
at random
is called a CANONICAL ENSEMBLE.
And the set of all possible states
of a system
in contact with
a reservoir
with which it can exchange
both energy (U) and particles (N)
is called a GRAND CANONICAL ENSEMBLE.
If the utility of these concepts is less than obvious to you, join the club. I won't need to use them to derive the good stuff below, but now you will be able to scoff at pedants that pretend you can't understand "Stat Mech" unless you know what the various types of Ensembles are.