# 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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