Dice Theorem
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Description: How many ways are there of throwing n indistinguishable dice each with m faces?
How many ways are there of throwing two indistinguishable dice? The answer is 21. Why? Answer: There are 6 ways of throwing the first die, and 6 ways of throwing the second die, and since the die throws are independent, there are 6*6 = 36 possibilities. But a 2 and a 3 is the same as a 3 and a 2 (if the dice are indistinguishable), so there are in fact less than 36 ways of throwing two dice. Of the 36 possibilities (when the dice are distinguishable) 6 are pairs of one number (1 plus 1, etc.). That leaves 30 where the dice have different numbers, so there are 30/2 = 15 possible results (when the numbers are different) if we do not distinguish one die from the other. These 15, plus the 6 results when the numbers are the same on each die, give 21.
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