(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 nN 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=106, 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≫N, both the BE and the FD results are approximately equal to nN/N!, which is 1/N! times the MB result.