Red, orange, yellow, green and blue balls
You have a bag with 1 red ball, 2 orange balls, 3 yellow balls, 4 green balls, and 5 blue balls.
You pick three out (without replacement) at random.
The probability each is a different color is \(\dfrac ab\), where \(a\) and \(b\) are coprime positive integers.
What is \(a+b\)?