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Omni-MATH / Herbert rolls 6 fair standard dice and computes the product of all of his rolls.…

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problem

Herbert rolls 6 fair standard dice and computes the product of all of his rolls. If the probability that the product is prime can be expressed as ab\frac{a}{b} for relatively prime positive integers aa and bb, compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
Herbert rolls 6 fair standard dice and computes the product of all of his rolls. If the probability that the product is prime can be expressed as (a)/(b) for relatively prime positive integers a and b, compute 100a+b.
Original LaTeX notation
Herbert rolls 6 fair standard dice and computes the product of all of his rolls. If the probability that the product is prime can be expressed as $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100 a+b$.

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