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"three instances" is correct and usable in written English.
You can use it to refer to three separate occurrences or happenings, especially those of the same kind. For example, "We have encountered three instances of racism within our organization."
Exact(60)
These three instances are not unique.
That's three instances, and three's a trend.
Three instances of this problem are considered.
Putnam said it identified three instances of market timing.
N.A.S.D. officials said they had uncovered the three instances in routine audits.
The recent trial focused on three instances where the police were accused of framing gang members.
Anderson said the umpire, Dan Iassogna, wrote that Anderson had used profane language in three instances.
He found three instances where two species on different islands made webs with similar architectures.
In all three instances, none of the patients had any memory of the act.
In three instances this season, front-office officials have stepped into the coaching vacuums.
It identified three instances of non-compliance with how it held data.
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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