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The phrase "allowed number of" is correct and usable in written English.
It can be used when referring to a specific quantity that is permitted or authorized in a given context.
Example: "The allowed number of participants for the workshop is limited to twenty."
Alternatives: "permitted quantity of" or "authorized amount of".
Exact(60)
The dusty old machines would not permit more than the allowed number of votes.
An alternative algorithm for specifying the allowed number of false sources detected has been added to this tool.
Legal challenges remain related to his dual military-civilian role, as well as to whether he had already served the constitutionally allowed number of terms.
The suggested Ugly Deal would sharply reduce the allowed number of operating Iranian centrifuges to a range of 1,000 to 3,000.
When the fire-management team reached its maximum allowed number of days in the field and was rotated out, another, more experienced team was brought in.
A proximity operator is a way of specifying that two terms in a query must occur close to each other in a document, where closeness may be measured by limiting the allowed number of intervening words or by reference to a structural unit such as a sentence or paragraph.
This indicator is related to the maximum allowed number of users in a femtocell.
Therefore, the maximum allowed number of the streptavidin biotinylated DNA within a 50 nm NW is less than 3.
Such sanctions result when the allowed number of tents for lodging tourists is not respected by the residents.
Because the WAVA is non-convergent, the maximal allowed number of iterations is set as 20 during the decoding process.
Lotus's Pastor Maldonado will take a 10-place grid penalty for using more than the allowed number of engine components.
More suggestions(16)
allowed incidence of
allowed employment of
allowed outcome of
permitted number of
allowed breakdown of
limitations number of
possible number of
followed number of
permit number of
permission number of
grant number of
authorized number of
enabled number of
permissible number of
tolerated number of
admissions number of
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com