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What is the probability that in 3,000 coin tosses of an unbiased coin 1,560 comes up heads and 1,440 comes up tails? Use Stirling's approximation

What is the probability that in 3,000 coin tosses of an unbiased coin 1,560 comes up heads and 1,440 comes up tails? Use Stirling's approximation to compute factorials for large numbers. Notice that 1,560 = 0.52 * 3,000 and 1,440=.0.48*3,000.

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