Posted by **John** on Monday, March 4, 2013 at 12:27am.

A 12 by 12 by 12 cube has all its faces painted blue. It is then broken down to 1728 individual 1 by 1 by 1 cubes. The probability that a randomly chosen 1 by 1 by 1 cube has exactly 2 faces painted blue is \frac {a} {b} , where a, b are coprime. What is the value of a+ b?

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