Regex to match (same-length) permutations of AAB -

hello stackoverflow community!

i want match (same-length) string permutations of aab, want match:

aab baa aba 

but not:

abb ab aaba 

i have found many sources mentioning lookarounds , backreferences @ similar questions such [1] or [2] struggling repeated characters such "aa".

i have tried:

^(?=[aab]{3}$)(?!.*(.).*\1).*$ ^([aab])(?!\1)([aab])(?!\1|\2)([aab])(?!\1|\2|\3)$ 

do have ideas on that? in advance!

here's pattern matches 3 permutations:

^(?=.*b)(?=(.*a){2})...$ 

this pattern requires that:

• the length of string 3 (...)
• there 1 b (the (?=.*b) lookahead)
• there 2 as (the (?=(.*a){2}) lookahead)

but wouldn't simpler ^(aab|aba|baa)$ work?