The correct order of the stoichiometries of $AgCl$ formed when $AgNO_3$ in excess is treated with the complexes: $CoCl_3 \cdot 6NH_3$, $CoCl_3 \cdot 5NH_3$, $CoCl_3 \cdot 4NH_3$, respectively, is:

According to Werner's theory, the central metal ion (Cobalt, $+3$) has a fixed secondary valency (coordination number) of 6. Species inside the coordination sphere are non-ionisable, while halide ions outside the sphere are ionisable and precipitate with $AgNO_3$.

1. $CoCl_3 \cdot 6NH_3$: Written as $[Co(NH_3)_6]Cl_3$. All three $Cl^-$ ions are outside the coordination sphere (primary valency only). Thus, 3 moles of $AgCl$ are formed.
2. $CoCl_3 \cdot 5NH_3$: Written as $[Co(NH_3)_5Cl]Cl_2$. One $Cl^-$ is inside (secondary valency) and two are outside. Thus, 2 moles of $AgCl$ are formed.
3. $CoCl_3 \cdot 4NH_3$: Written as $[Co(NH_3)_4Cl_2]Cl$. Two $Cl^-$ ions are inside and one is outside. Thus, 1 mole of $AgCl$ is formed .