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The phrase "predetermined number of" is correct and usable in written English.
You can use it when you want to refer to an exact amount or quantity of something that has already been established. For example: "The winner of the contest will be determined by a predetermined number of points."
Exact(59)
The presentation ceases after either a predetermined number of calls or after the subject shows no discernible response in a number of presentations.
In some cases — primarily overseas — the time share is available on a lease for a predetermined number of years.
A predetermined number of deals are played, and the cumulative score determines the winner.
In each of 100 levels, you must intercede to rescue a predetermined number of lemmings by shepherding them to hot-air balloons before a clock runs out.
Truth is, the road to stardom is littered with "bringer" shows, in which the beginner is booked only on condition of bringing a predetermined number of paying customers.
As for race modes, there are the checkpoint races, which challenge a gamer to pass through a predetermined number of checkpoints before time runs out.
Lasa proposed that each player be allowed a bank of time in which to play a predetermined number of moves, such as two hours for 30 moves.
When the predetermined number of revolutions had occurred, the wings of the airplane were dropped off and the aircraft carrying the bomb load dropped on the target.
"The system is capable of recognizing a predetermined number of various hand gestures and is capable of tracking movement of the user's hand and individual fingers," the inventors write.
In March, the bank and the Mexican Finance Ministry said that the reserves were getting too big and expensive to hold, and announced that a predetermined number of dollars would be sold daily to limit the size of the hoard.
With such a mortgage, Mr. Eisenson said, the lender calculates how much the monthly payment needs to be to repay a specific amount for a predetermined number of years at a fixed interest rate.
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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