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Its said that the probability of having the configuration of ##n## particles in the left side is given as ##P_n=C(n)/2^N## with ##C(n)## being the total number of ways in which ##n## particles from ##N## can be placed in the left side.

Why should ##P_n=C(n)/2^N## be the probability? It should be true only if each configuration is equiprobable, but I don't think it is equiprobable.

Our initial conditions (position and velocity of particles) will determine the evolution of the states of the system, so it might be that some states occur more frequently than other and some might never occur?