206. 
Two threeletter strings, and , are transmitted electronically. Each string is sent letter by letter. Due to faulty equipment, each of the six letters has a 1/3 chance of being received incorrectly, as an when it should have been a , or as a when it should be an . However, whether a given letter is received correctly or incorrectly is independent of the reception of any other letter. Let be the threeletter string received when is transmitted and let be the threeletter string received when is transmitted. Let be the probability that comes before in alphabetical order. When is written as a fraction in lowest terms, what is its numerator? This problem is copyrighted by the American Mathematics Competitions.

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