Fermions and bosons demonstrate different distribution statistics over a set of quantum states. However, in Chapter 31 we will encounter the Boltzmann distribution, in which we essentially ignore the differentiation between fermions and bosons. This is appropriate only in the “dilute limit,” where the number of available states far outnumbers the number of particles. To illustrate this convergence:

a. Determine the number of arrangement permutations possible for 3 bosons and 10 states, and repeat this calculation for fermions.

b. Repeat the calculations from part (a) for 3 particles, but now 100 states. What do you notice about the difference between the two results?