Doubt from probability

moderate
probability
cubes
unsolved
pp
#1

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.
Give it a try.
Thanks
(Please provide detailed solution)

#2

74?
@Tushar_2019

{5^{12}}\over{3^{18}.2^{34}}

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#3

Yup @Soumyadeep_2019 , submit detailed solution

#4

Answer is 74, we calculate all possibilities of occuring of four faces painted orange.

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