Ordered Balls

A bag contains \(150\) balls numbered \(1\) through \(150\). Three balls are drawn and placed on the table. The probability that the balls were drawn in increasing order can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

Details and assumptions

The balls are drawn in increasing order if each subsequent ball is a higher number. As an explicit example, drawing balls \( 1, 10, 100 \) in that order is considered an increasing order.

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