Find The Rainbow

Seven balls of different weights are randomly painted red, orange, yellow, green, blue, indigo and violet, each ball being painted a distinct color.

The green ball is found to be heavier than the blue ball, and the red ball is found to be heavier than the yellow ball.

Given just this information, if the probability that the red ball is heavier than the blue ball is \(\dfrac{a}{b}\), where \(a,b\) are coprime positive integers, find \(a + b\).


Inspiration.

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