data structures - Random Partition - pivot is median of three random elements probability

Question

The Question and the answer

The Question and the answer is from "Introduction to Algorithms" by Cormen, Leiserson, Rivest and Stein. in the chapter on Quick-Sort.

when they calculated the probability, they came up to the expression 2(a^3+3a^2(1-a)) (marked in red).

how did they come up to this expression?

question from:https://stackoverflow.com/questions/65849579/random-partition-pivot-is-median-of-three-random-elements-probability

Answer 1

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