Rolling four die

Discrete Mathematics Level pending

Ruby McTube has four six sided die.

They each have the following numbers on their six faces: \(1,1,2,2,4,6\)

If she rolls all four, the probability they each show a different number on top is \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers.

What is \(a+b\)?

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