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Calculus Level 5

Suppose \(9\) real numbers are chosen uniformly and at random from the interval \([0,1]\). Let \(W\) be the variable measuring the (magnitude of the) difference between the greatest and least of the \(9\) randomly chosen numbers.

If the expected value \(E[W] = \dfrac{a}{b}\), where \(a, b\) are positive coprime integers, then find the product \(a*b\).

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