Three Dice, Total Spread Six

Problem

A fair six-sided die with faces numbered $1$ through $6$ is rolled three times, the rolls being independent, giving results $a_1, a_2, a_3$ in order. Find the probability of the event

|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_1| = 6.

Answer

Solution

Difficulty	5/10
Topics	Counting, probability, Casework

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