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The phrase "a finite pool of" is correct and usable in written English.
It can be used when discussing limited resources, options, or choices available in a particular context.
Example: "In a competitive market, companies often find themselves competing for a finite pool of customers."
Alternatives: "a limited number of" or "a restricted set of".
Exact(25)
"It's a finite pool of money," he said.
"There is a theory that there is a finite pool of worry that anyone has".
It has a finite pool of money in which to pay out claims if it is to be self-sustaining.
Anyway, there is a finite pool of creative talent and we would struggle to supply significantly greater hours of value or quality.
High schools are drawing from a finite pool of students and should not be held to the same standards as colleges, he said.
Each of us has what Elke Weber, the co-director of the Center for Research on Environmental Decisions, describes as a "finite pool of worry," and we tend to fill it with immediate personal concerns.
Similar(35)
"When you think about the future of search broadly, I see it bifurcating between what I would think of as more tactical queries where you have a question and there's one right answer or a small finite pool of good answers," Corsell said.
While a hyperbola can model sampling of gene phamilies from a finite pool, it does not accommodate the influx of new phamilies.
Some studies have suggested the possibility that new follicles with oocytes may form in adulthood [21], [22], [23], but the preponderance of literature suggests that a defined and finite pool of primordial follicles exists [24].
Participants in a prediction market run by the BRAIN process can place bets from their finite pool of betting tokens on the possibility that various outcomes might occur.
By competing for the same finite pool of microRNAs, ceRNA regulate each other.
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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