A discrete mathematics problem by Aira Thalca

6 different balls are to be placed in three different boxes A, B, C. Each ball is placed uniformly at random in one of these boxes. The probability that box A will contain exactly 3 balls can be written as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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