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I am trying to follow the Particle Data Group's instruction (PDF link) to combine SU(N) multiplets. On page 3, they show an example calculation of SU(3)'s $\textbf 8\otimes \textbf 8$.

I understand step (b), i.e. how to add the $a$'s, but then for the next step, why is there no diagram like this,

[ ][ ] a a b
[ ]

i.e. a $(4,1)$ multiplet of multiplicity $\textbf{35}$?

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Counting from right to left the number of a’s must always be greater than the number of b’s.

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