Suppose we have a system of 3 particles, each of which can be in one of three states, A, B, and C, with equal probability. Write an expression that represents all of the possible configurations of the entire system, and determine which configuration will be most likely (such as "2 particles in state A, one in state B").

Return to the binary system discussed before. If the system consists of 5 particles, how many states of the entire system have 3 magnets in the up position?

Take a system with 20 possible states, all equally likely. What is the probability of being in any particular state?

In certain quantum scenarios, there are two distinct energy levels that a particle may occupy. Let one of the levels have an energy U which is equal to U₁ = ω, and let the other level have energy U₂ = 2ω. Let us further suppose that the particle is twice as likely to be in level 1 than in level 2. What is the average value of the energy?

State the Fundamental Assumption, and explain how it is related to the function P(s).