# 6 Dice Arrangement

Six standard six-sided dice are rolled. Let $$p$$ be the probability that the dice can be arranged in a row such that for $$1 \leq k \leq 6$$ the sum of the first $$k$$ dice is not a multiple of 3. Then $$p$$ can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

Details and assumptions

You get to choose the order that the dice is arranged. For example, if the dice thrown was $$\{ 1, 1, 1, 2, 2, 3\}$$, then we can reorder them as $$( 1, 1, 2, 1, 2, 3)$$ which satisfies the conditions.

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