A discrete mathematics problem by Nicholas Tomlin

Five distinct numbers are randomly chosen from the set \( S = \{0,1,2,3,4,5,6,7,8,9\} \) and multiplied. The likelihood that the product is even can be written as \( \frac{a}{b} \), where \( a, b \) are relatively prime positive integers. Find \( a + b \).

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