The trap that costs marks here: confusing the coordination number with the total number of ions or atoms attached to a metal. Counter-ions sitting outside the coordination sphere are not ligands — counting them inflates the coordination number and leads straight to a wrong answer.
What a ligand actually is. A ligand is a neutral molecule or ion that donates at least one lone pair of electrons to a central metal atom or ion, forming a coordinate bond (NCERT Class 12 Chemistry Chapter 5, page 4). The metal is the Lewis acid; the ligand is the Lewis base. Only species directly bonded to the metal inside the coordination sphere count.
Denticity — how many donor atoms one ligand has. A monodentate ligand (Cl⁻, NH₃, H₂O) donates through one atom. A bidentate ligand (ethylenediamine, oxalate) donates through two atoms. Polydentate ligands like EDTA⁴⁻ donate through six atoms. Denticity matters because the coordination number equals the total number of donor atoms, not the total number of ligand molecules.
Coordination number. It is the number of ligand donor atoms directly bonded to the central metal ion. For [Co(NH₃)₆]³⁺, six monodentate NH₃ molecules give coordination number 6. For [Co(en)₃]³⁺, three bidentate ethylenediamine ligands still give coordination number 6 (3 ligands × 2 donor atoms each). The counter-ions (Cl⁻ outside the bracket in [Co(NH₃)₆]Cl₃) do not count.
Primary vs secondary valency (Werner's theory). Primary valency is the oxidation state — satisfied by counter-ions and ionizable. Secondary valency is the coordination number — satisfied by ligands and fixed for a given complex. NEET questions frequently ask you to distinguish these: a common distractor treats all attached species as ligands, conflating primary and secondary valencies.
Watch-out: When a formula like CoCl₃·6NH₃ is written without brackets, identify which species are inside the coordination sphere (ligands) and which are ionizable counter-ions before assigning the coordination number.