This tiling problem may not be what you expect

Discrete Mathematics Level pending

Bob is painting his tiles, and he plans to color each tile with one of 6 different colors. He paints a group of 12 tiles randomly (true random), and notices that no more than 3 distinct colors showed up on the tiles, out of the possible 6. The probability that this scenario occurs can be expressed as a/b, for coprime a and b. Enter your answer as a+b.

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