Help Joe find a+b

Discrete Mathematics Level pending

Joe picks \(2\) distinct numbers from the set of the first \(14\) positive integers \(S = \{1,2,3,\ldots,14\}\). The probability that the sum of the \(2\) numbers is divisible by \(3\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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