Suppose that 10 dice are rolled. Each die is a regular 6 -sided die with numbers 1 through 6 labelled on the sides. How many different sums of all 10 numbers are possible?

Answer 1

smallest sum is 10, largest sum of 600

since all possible sums between are possible,
all we have to do is find which term number 600 is
of the arithmetic sequence with
term1 = 10 , d = 1, term(n) = 600
a + (n-1)d = term(n)
10 + n-1 = 600
n-1 = 590
n = 591

There are 591 different sums possible.