Concept:
In coordination compounds, the oxidation state of the central metal ion can be determined using the charges of ligands and the overall charge of the complex.
Important points:
• \(NH_3\) is a neutral ligand.
• \(Cl^{-}\) carries a charge of \(-1\).
• The compound \([Co(NH_3)_6]Cl_3\) contains three chloride ions outside the coordination sphere.
Step 1: Determine the charge on the complex ion.
Since there are \(3\) chloride ions \((Cl^-)\), the complex ion must have a charge of:
\[
[Co(NH_3)_6]^{3+}
\]
Step 2: Let the oxidation state of cobalt be \(x\).
\[
x + 6(0) = +3
\]
Step 3: Solve the equation.
\[
x = +3
\]
Thus, the oxidation state of cobalt is:
\[
\boxed{+3}
\]