Step 1: Understand the name of the complex.
The complex is pentaammine aqua cobalt(III) iodide.
This indicates that cobalt is in the +3 oxidation state and is coordinated with five ammonia molecules and one water molecule.
Step 2: Determine charge on the complex ion.
Ammonia and water are neutral ligands.
Cobalt is in the +3 oxidation state, so the complex ion has a charge of \(+3\).
Step 3: Balance with counter ions.
To neutralize the +3 charge, three iodide ions \((\text{I}^-)\) are required outside the coordination sphere.
Step 4: Final structure.
Thus, the correct formula is:
\[
[\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]\text{I}_3
\]
Step 5: Conclusion.
Option (A) correctly represents the coordination compound.