So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?
Suppose that we roll a six-sided die ten times. What is the probability
that the total of all ten rolls is divisible by six?
Best Answer
Hint.
Roll $9$ times and let $x$ be the total.
For exactly one number $n\in\{1,2,3,4,5,6\}$ we will have $6 \mid (x+n)$ (i.e. $x+n$ is divisible by $6$).