# Unto zero

Discrete Mathematics Level 3

Let $$a, b$$ and $$c$$ be the three numbers resulting from three independent throws of a fair 6-sided dice labeled $$1$$ through $$6$$. The probability that $$(a-b)(b-c)=0$$ 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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