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Suppose we have three fair 6-sided die (one colored green, one colored black, and one colored red). An experiment consists of rolling all three die. Let G, B, and R denote the numbers rolled on the green, black and red die respectively.

(a) What is the probability that no two of these die show the same number after the roll?

(b) What is the conditional probability that G < B < R given that no two dice show the same number? (Hint: You might consider using symmetry, and consider how many orderings of G,B,R are possible when they are different numbers).

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