seat arrangement possibilities What could be possible arrangements for the below?    

A, B, C, D and E are sitting on a bench. A is sitting next to B, C is
  sitting next to D, D is not sitting with E who is on the left end of
  the bench. C is on the second position from the right. A is to the
  right of B and E. A and C are sitting together.

 A: According to the given information that 


*

*$E$ is on the left end of the bench and

*$C$ is on the second position from the right
you know that the $5$ places on the bench look like $$\underline{\color{blue}{E}}\,\underline{}\,\underline{}\,\underline{\color{blue}{C}}\,\underline{}$$ 


Now, consider the information that 


*

*$A$ is next to $B$ and that

*$A$ is on the right of $B$ (and $E$)


which implies that the only possibility to place $A$ and $B$ is the following
$$\underline{E}\,\underline{\color{blue}{B}}\,\underline{\color{blue}{A}}\,\underline{C}\,\underline{}$$ This leaves one empty position to place $D$ on the right end
$$\underline{E}\,\underline{B}\,\underline{A}\,\underline{C}\,\underline{\color{blue}{D}}$$

Note however that some of the information that you were given was not useful (or redundant) as for example that $A$ is on the right of $E$, that $E$ does not sit next to $C$ and that $A$ is next to $C$. These clues were implied by the rest. 
A: $E$ is on the left end and so we first place $E$ and let the initial arrangement be $$E\star\star\star\star$$
After that we fix the position of $C$, then it becomes, $$E\star\star C\star$$ After that we fix the position of $D$, then we  get,$$E\star\star CD$$ 
Then we fix $A$,
$$E\star A CD$$
Lastly $B$,
$$\boxed{EB A CD}$$
