A question I encountered recently :
A six digit number divisible by $3$ is to be formed using the digits $0,1,2,3,4$ and $5$ without repetition. How many number of ways can this be done ?
If it asked for numbers divisible by $2$, I know how to proceed -- the last digit could be $0, 2$ or $4$. But I have no idea how to do this problem.