Problem 4: a) Use the strong form of the Sterling approximation to compute the probability of getting exactly 500 heads and 500 tails. Even if you have access to a way to compute the factorial of 1000, do not do the exact calculation, use the Sterling approximation. Use the strong form of Sterling's approximation, In N! = N In N – N +;In 27N , to solve this problem. b) Use Sterling's approximation (strong form) to compute the probability of getting exactly 600 heads and 400 tails.

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