The Stirling approximation, is very handy when dealing with numbers larger than about 100....

The Stirling approximation, is very handy when dealing with numbers larger than about 100. Consider the following ratio: the number of ways N particles can be evenly divided between two halves of a room to the number of ways they can be divided with 60% on the right and 40% on the left. (a) Show, using the Stirling approximation, that the ratio is approximately (400.460.6/5)N for large N, (b) Explain how this fits with the claim that average behaviors become more predictable in large systems.