Probability of sum to be divisible by 7 6 fair dice are thrown simultaneously. What is the probability that the sum of the numbers appeared on dice is divisible by 7 ?

One way is to add the coefficients of $x^7+x^{14}+x^{21}+x^{28}+x^{35}$ in the expression $(x+x^2+x^3+x^4+x^5+x^6)^6$ which will be symmetrical around the middle.
Another way is to use stars and bars, and apply inclusion-exclusion by preplacing $6$ in one or more of the $6$ cells, e.g. for a sum of $21$,
$\binom{20}{5} - \binom61\binom{14}{5} + \binom85 = 4332$
Once you have the number of favorable ways, you can compute $Pr$ 
