i) For a system of 3 distinguishable particles distributed in two similar compartments, the total number of microstates corresponding to the condition that no compartment should remain empty are______.
a) 4, b) 6, c) 3, d) 9.
As particles are distinguishable, the possible states depend on the position of each particle, where the position means just in which compartment they are situated. The number of possible states is , as it is . Now we need to exclude the states where one compartiment is empty : there is exactly two such states :
Therefore there is microstates where no compartment is empty.
The answer is b.
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