Chapter 16, Problem 12P

* Nine numbered balls are dropped randomly into three boxes. The numbers of balls falling into each box are labeled $n_1\text{, }{n}_2\text{, and }{n}_3\text{.}$

(a) Identify five of the many possible arrangements or macrostates of the balls. (b) Determine the ratio of the count for the equal distribution $\left(n_1=3,n_2=3,\text{ and }{n}_3=3\right)$ and for the 0, 0, 9 distribution. (c) Determine the ratio of the count for the equal distribution and for the 2, 3, 4 distribution. Note The count is given by

$\Omega =\frac{n!}{n_1!n_2!n_3}$ where n is the total number of balls.