# 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.

×