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The phrase "a fortuitous set of" is correct and usable in written English.
It can be used to describe a fortunate or lucky collection of items, events, or circumstances that have come together unexpectedly.
Example: "The researchers discovered a fortuitous set of data that provided new insights into the phenomenon."
Alternatives: "an unexpected collection of" or "a lucky assortment of".
Exact(2)
Last week, through a fortuitous set of circumstances, I had the magnificent chance to speak to the Purdue football team, struggling through a tough losing season.
The consortium came together through a fortuitous set of circumstances.
Similar(58)
The authors take advantage of a fortuitous data set, and use an ordered probit-model to compare the score given by expert peer reviewers to 11,500 research articles (i.e., Excellent-A; Good-B; Fair-C; Limited-D) and the rating of the journal (classified as A or non-A) in which the individual articles were published.
Scientists monitoring a joint European Space Agency (ESA)–NASA solar probe in the waning months of its 18-year mission have collected a fortuitous but startling set of data.
I was disappointed to concede the first try from a set piece and the second was a fortuitous bounce of the ball so we let the game get away.
Then a fortuitous series of events converged.
It is a fortuitous collision of man and moment.
They met at GQ in 1992, a fortuitous unification of fellow travelers.
Heirlooms began as hybrids, after all — a fortuitous cross of two parents.
The assault was attempted on Sept. 17, a fortuitous bit of planning, considering it snowed the next day.
So the First Folio and the first Americans became informally twinned in a fortuitous assertion of originality.
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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