Consider a collection of 10 ordinary six-sided dice with face values 1 through 6. Each die is a completely regular cube. They are thoroughly shaken and tossed onto a table. Answer the following:
What is the least probable value(s) of the sum of the dice?
What is the most probable value(s) of the sum of the dice? Provide a logical argument for your answer to this last question, rather than a detailed listing of states.
What is the mean or average value for the sum of the dice?
Now consider a collection of 5 "Fermi" dice. That is, no two dice may have the same face up. (This may be accomplished by randomly tossing the dice sequentially and re-throwing any die that comes up with a face value already present on the table.) Answer the previous three questions for this case.
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