2005 AIME I Problems/Problem 9
Problem
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 
cube. Given the probability of the entire surface area of the larger cube is orange is 
where 
and 
are distinct primes and 
and 
are positive integers, find 
Solution
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