We roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by 6? 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?
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 $6$).
Couldn't you also think of it as the maximum possible value you could get for rolling the die 10 times would be 60, how many numbers between 1 and 60 are divisible by 6? 10 numbers are divisible by 6(6*1, 2, 3, etc.)  So, 10 out of 60 possible values gives... 1/6.  I love math.