Concept:
• Coordination number is the number of ligand donor atoms directly bonded to the central metal ion.
• Oxidation state of the central metal ion is calculated using the overall charge of the complex and the charges of the ligands.
Step 1: Determine the coordination number.
In the complex ion:
\[
[Co(NH_3)_6]^{3+}
\]
There are six \(NH_3\) ligands attached to the cobalt atom.
Since each \(NH_3\) acts as a monodentate ligand, the coordination number is
\[
\boxed{6}
\]
Step 2: Determine the oxidation state of cobalt.
Ammonia \((NH_3)\) is a neutral ligand, so it contributes 0 charge.
Let the oxidation state of cobalt be \(x\).
\[
x + 6(0) = +3
\]
\[
x = +3
\]
Thus, the oxidation state of cobalt is
\[
\boxed{+3}
\]