Chapter 9, Problem 21E

Consider a room divided by imaginary lines into three equal pans. Sketch a two-axis plot of the number of ways of arranging particles versus $N_{\text{left}}$ and $N_{\text{right}}$ for the case $N={10}^{23}$ . Note that $N_{\text{middle}}$ is not independent, being of course $N-N_{\text{right}}-N_{\text{left}}$ . Your axes should be $N_{\text{left}}$ and $N_{\text{right}}$ , and the number of ways should be represented by density of shading. (A form for numbers of ways applicable to a three-sided room is given in Appendix J, but the question can be answered without it.)