10 Stones

Ten stones all have distinct weights.

They are randomly labeled A through J.

The stone labeled B is weighed against all the other stones except J, and found to be heavier than all of them except A.

The probability that J is heavier than B is given as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers.

What is \(a+b\)?


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