In aaabbbb there were 3 'a's and 4 'b's.
In ab there were 4 'a's and 5 'b's.
In abb there were 5 'a's and 7 'b's.
In aabb there were 7 'a's and 9 'b's.
In aaabb there were 10 'a's and 11 'b's.
In aabbb there were 12 'a's and 14 'b's.