Twenty seven unit cubes are painted orange on a set of four faces so that two non-painted faces share an edge. The 27 cubes are randomly arranged to form a 3\times 3 \times 3 cube. Given the probability of the entire surface area of the larger cube is orange is \frac{p^a}{q^br^c}, where p,q, and r are distinct primes and a,b, and c are positive integers, find a+b+c+p+q+r.

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# Doubt from probability

**Tushar_2019**#1

**Shiva_1**#4

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