[math]2n[/math] balls are chosen at random from a total of [math]2n[/math] red balls and [math]2n[/math] blue balls. Find a combinatorial expression for the probability that the chosen balls are equally divided in color. Use Stirling's formula to estimate this probability. Using BinomialProbabilities, compare the exact value with Stirling's approximation for [math]n = 20[/math].