Suppose you have three particles, and three distinct one-particle states $\left(\psi_{a}(x), \psi_{b}(x)\right.$, and $\left.\psi_{c}(x)\right)$ are available. How many different three-particle states can be constructed (a) if they are distinguishable particles, (b) if they are identical bosons, and (c) if they are identical fermions? [The particles need not be in different states- $\psi_{a}\left(x_{1}\right) \psi_{a}\left(x_{2}\right) \psi_{a}\left(x_{3}\right)$ would be one possibility if the particles are distinguishable.]