# Thread: Dice Problems - Permutations and Combinations

1. ## Dice Problems - Permutations and Combinations

1.How many possible sums can you roll if you have the choice to use at most 3 dice? You must use at least one die.

2.If you were to roll 5 dice each 5 times, how many possible outcomes are there?

2. ## Re: Dice Problems - Permutations and Combinations

Originally Posted by Unrated063
2.If you were to roll 5 dice each 5 times, how many possible outcomes are there?
I agree that #1 is trivial. But I am not sure that the first reply is correct about #2.
To me it clear that five dice are rolled five times. The sums on each roll are summed to give a total.

This is the expansion of the generating function.
Look at the exponents in that expansion, they range from $25\text{ to }150$
Next look at the coefficient of each term. One of the terms is $130616265x^{35}$.
From which we now know that there are $130616265$ ways to get the sum $35$.

The sum of all the coefficients gives the total possible outcomes.