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Consider an ensemble consisting of five distinguishable (e.g. different colored) dice.
a. What is the total number of different outcomes that can be obtained by throwing all five dice at once? Generalize your result to N distinguishable dice.
b. How many different ways can a roll consisting of {2, 3, 4, 2, 1} be achieved? Repeat for a roll of {3, 3, 3, 5, 5}.
c. What is the probability of obtaining each result in part b? 

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