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Find the probability of rolling ten different, standard 6-sided dice simultaneously and obtaining a sum of 30?
I started to answer this question by setting up an equation like this:
x1+x2+...+x10=30 with 0 less than or equal to xi less than or equal to 6 But we know the die will have values 1-6 so we have y=x+1 so that y1+y2+...+y10=20 Now I know we can have at most 4 6's, 5 5's, 6 4's, 10 3's, 10 2's, 10 1's.
I was not sure if I am heading in the right direction or should I just find all possible outcomes of the die and use the inclusion-exclusion method to find all the permutations in which the sum will be 30?