Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?


A. \(\frac{1}{336}\)

B. \(\frac{1}{2}\)

C. \(\frac{17}{28}\)

D. \(\frac{3}{4}\)

E. \(\frac{301}{336}\)


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