Is it grammatically correct to write
"based on an available of an item or a service?"
If it is wrong, how about 'based on the available of an item or a service?"
please help me.
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Available is not a noun and following sentences you wrote are incorrect:
Based on an available of an item or a service
Based on the available of an item or a service
Grammatical sentences are:
Based on the availability of an item or a service
Based on the assumption that an item or a service is available (as WhatRoughBeast has said)
You can also write:
(It is) based on whether or not an item or a service is available.
Here, you can use the adjective 'available' in the sentence.