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The phrase "a possibility of a solution" is correct and usable in written English.
It can be used when discussing potential options or outcomes in problem-solving contexts.
Example: "After reviewing the data, we found a possibility of a solution that could address the issue effectively."
Alternatives: "a chance of a solution" or "an option for a solution".
Exact(1)
He was never afraid of opening up debate and talking things through until there was a possibility of a solution.
Similar(59)
Apart from a brief mention on a website operated by Libyan dissidents, the cable adds, it was "noteworthy that the news was kept out of the press," since "all parties involved -- including the foreign companies -- had an interest in keeping things quiet as long as there seemed a possibility of a near-term solution".
It seems to me there is a possibility of some solution if the Iranians are prepared to not move toward nuclear weapons, and to pursue a nuclear program under the non-proliferation treaty with full transparency and I.A.E.A. inspections.
The possibility of a solution seems remote.
Instead several of these riddles combine, and through their interaction the possibility of a solution takes shape.
Then, with the news I had brought her, came the possibility of a solution to the problem.
Harry Bailey, an independent from Gresham, Ore., a retiree and military veteran, said he was pessimistic about the possibility of a solution.
Jeffrey Goldberg has written, in The Atlantic, that the real provocation for the knife attacks is a century-old "Palestinian narrative, one that obviates the possibility of a solution that allows Jews national and religious equality".
But last week, a groundbreaking deal by Clear Channel Communications, the country's largest radio broadcaster, raised the possibility of a solution to the standoff through marketplace negotiations instead of political head-butting.
The only possibility of a solution resides in collective shift or, as he said, "a real change in the system".
Nearly as many are also disillusioned and deeply cynical about the possibility of a solution in the near future.
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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