Roll the dice thrice 2

A fair dice is numbered with 1, -2, 0, -1, 3, 2 on its faces.

Let the probability of getting a sum of 5 after rolling the dice thrice can be expressed as \(\frac{a}{b}\) where \(a,b\) are relatively coprime positive integers.

Find \(a+b\) .

Try these too: Part I, Part III.
Image Credit: Flickr Gard Rimestad.

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