Tag Archives: combinatorics

The “dice roll with a given sum” problem

In some exercise taken from combinatorics textbooks you might find a question like: “if you roll 2 dice what is the probability to get 9 for the sum of the 2 dice faces?
The answer is not much difficult and can be intuitively given by enumerating the number of cases that satisfy the given event and dividing that number with the number of all possible outcomes.
But what if you want to find the probability of, say, a sum of 31 when rolling 10 dice, where simple enumeration would require a very long time? Or to find a more general formula for the probability of getting p points as the sum of rolling n dice? Is there such a formula, computable without having to enumerate all the cases?

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