External course, beginning at the wrong end (5)

I believe the answer is:

outer

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'external' is the definition.
(similar in meaning)

'course beginning at the wrong end' is the wordplay.
'course beginning at' becomes 'out' (I can't explain this - if you can you should believe this answer much more).
'the wrong' becomes 'err' (to err is make an error).
'end' says to hollow out the word (remove centre letters) (I've seen 'ends' mean this).
'err' with its centre taken out is 'er'.
'out'+'er'='OUTER'

Can you help me to learn more?

(Other definitions for outer that I've seen before include "External kind of route" , "Poor shot" , "Ring furthest from the bullseye" , "External; part of archery target" , "Surrounding" .)

I've seen this clue in The Times.

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