Balls in buckets

Start by regarding ball arrangements which can be rotated to each other as distinct. There are $7$ ways of putting all $3$ balls in the same bucket, $7\times6$ ways of putting $2$ balls in one bucket and $1$ in another, and $\binom{7}{3}$ ways of putting all $3$ balls in different buckets. That makes $84$ ways in all.

Now regarding arrangements the same if they can be rotated to each other, the $84$ above arrangements can be grouped into $12$ sets of $7$ , where each of the arrangements in a set of $7$ consists of the all the rotated variants of a particular arrangement. Thus, if we regard arrangements as the same if they can be rotated onto each other, there are $12$ possible arrangements of balls.