If adjacent is implied then we can answer the query using (1) and (3) only I think .
(1) CBE / EBC
(2) EB
(3) ADE / EDA
Now, If we take : CBE then ADE (Not feasible) so, only EDA
i.e. CBEDA ----> E is middle
Now, If we take : EBC then EDA (Not feasible) so, only ADE
i.e. ADEBC ----> E is middle
Hence, only (1) and (3) are sufficient !
Anything wrong above ?