Structural isomers of hexaammineiron(III) hexacyanidocobaltate(III) Find the number of structural isomers of $\ce{[Fe(NH_3)_6][Co(CN)_6]}$


This was a question solved by my teacher as follows: 

The $\ce{CN}$ will show linkage isomerism while $\ce{NH_3}$ and $\ce{CN}$ will show coordination isomerism.

We will now consider cases of coordination isomerism and then use linkage isomerism.


$\ce{[Fe(NH_3)_6][Co(CN)_6]}\rightarrow 7$ isomers(due to linkage isomerism of $\ce{CN}$)
$\ce{[Fe(NH_3)_5(CN)][Co(CN)_5(NH_3)]}\rightarrow 2\times 6=12$ 
$\ce{[Fe(NH_3)_4(CN)_2][Co(CN)_4(NH_3)_2]}\rightarrow 3\times 5=15$ 
$\ce{[Fe(NH_3)_3(CN)_3][Co(CN)_3(NH_3)_3]}\rightarrow$ not counted.


The further $3$ cases are similar to the first $3$ and will result in the same number of isomers. Hence the answer is $2\times(7+12+15)=68$.

Why is $\ce{[Fe(NH_3)_3(CN)_3][Co(CN)_3(NH_3)_3]}$ "not counted"? 

I feel that isomers due to $\ce{CN}$ showing linkage isomerism are perfectly valid. Please correct me if I'm wrong and sorry if the question is too trivial.
I have found the answer:


  In the following case:
  $$\ce{[Fe(NH_3)_3(CN)_3][Co(CN)_3(NH_3)_3]}$$
  Both the constituent entities are neutral and hence will exist independently, and thus will not form isomers of the original compound.