$A,B,C,D$ and $E$ are five persons who are to be seated around a circular table such that $A$ and $B$ must sit together and $C$ and $D$ must never sit together. In how many ways can they be seated?
First we make $(AB)$ and $E$ sit which can be done in $2$ ways since $A$ and $B$ can arrange themselves in $2!=2$ ways.
One of $C$ and $D$ can be put into gaps between $E$ and $A$ and the other can be put into the gap between $B$ and $E$ for which there are obviously $2$ ways.
To obtain total number of ways it appears that we should multiply number of ways in Step 1($=2$) and number of ways in Step 2($=2$) ways, i.e. total number of ways $=2\times 2=4$.
But it is easy to notice that in these $4$ ways two of the arrangements are rotation of the other two.
So should the answer be $4$ or should it be $2$.
In general what should be the approach?
Say we have $10$ persons sitting around a circular table with $3$ of them wanting to sit together only whereas $4$ other persons do not want to sit next to each other?
Should the rotation of a particular arrangement be construed as same or different?