Consider a collection of N molecules moving freely (and randomly) around in space, in a closed container of ?xed volume. We’re going to break that volume up into a series of subvolumes (or “bins”), and associate an “occupation number” with each bin, so that the values {a1, a2, . . .} represent the numbers of molecules in bin 1, bin 2, etc.

First consider just two bins, a1 and a2.

(a) Write an expression for W, the number of ways to distribute the molecules between the two bins (which could represent, say, the left and right halves of our volume, or the top and bottom). Without doing an explicit calculation, what con?guration would you expect to have the largest value of W (explain brie?y)?