Panama university department's backward? Pardon? (5,3)

I believe the answer is:

straw hat

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'panama' is the definition.
(synonyms)

'university department's backward? pardon?' is the wordplay.
'university department's' becomes 'arts' (I am not sure about this - if you are sure you should believe this answer much more).
'backward?' says the letters should be written backwards (I've seen 'backward' mean this).
'pardon?' becomes 'what' (I've seen this before).
'arts' written backwards gives 'stra'.
'stra'+'what'='STRAW-HAT'

Can you help me to learn more?

(Other definitions for straw hat that I've seen before include "Panama" , "Boater" , "Capital Investment?"" .)

I've seen this clue in the Sydney Morning Herald.

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