# Lucky Seven

Let $$S$$ be the set of non-negative integer triples $$(x,y,z)$$ that satisfy the equation $$x + y + z = 28$$. If a triple is chosen uniformly at random from $$S$$, then what is the probability that the product $$xyz$$ is divisible by $$7$$?

If the probability is $$\dfrac{a}{b}$$, where $$a,b$$ are positive coprime integers, then enter $$a + b$$ as your answer.

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