Suppose you have three particles, and three distinct one-particle states (ψa(x), ψb(x), and ψc(x)) are available. How many different three-particle states can be constructed, (a) if they are distinguishable particles, (b) if they are identical bosons, (c) if they are identical fermions? (The particles need not be in different states— ψa(x1) ψa(x2)ψa(x3) would be one possibility, if the particles are distinguishable.)
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