Chapter 15.4, Problem 19P

(a) Following the methods of Examples 3, 4, and 5, show that the number of equally likely ways of putting $N$ particles in $n$ boxes, $n>N,$ is $n^N$ for Maxwell Boltzmann particles, $C(n,N)$ for Fermi-Dirac particles, and $C(n-1+N,N)$ for Bose-Einstein particles.

(b) Show that if $n$ is much larger than $N$ (think, for example, of $n={10}^6,N=10$), then both the Bose-Einstein and the Fermi-Dirac results in part (a) contain products of $N$ numbers, each number approximately equal to n. Thus show that for $n\gg N$, both the BE and the FD results are approximately equal to $n^N/N!,$ which is $1/N!$ times the MB result.