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The phrase "all three participated" is correct and usable in written English.
You can use it when referring to a situation where three individuals or entities took part in an activity or event.
Example: "In the project, all three participated actively, contributing their unique skills to the team's success."
Alternatives: "all three took part" or "all three were involved".
Exact(7)
All three participated in a campaign to protest against the legal harassment of Özgür Gündem.
In November students from all three participated in the first Digital Humanities Conference for Undergraduates.
All three participated in a televised forum on Fox News moderated by former Arkansas Gov. Mike Huckabee, who was a top contender for the GOP nomination in 2008.
Saint Louis became the flagship of the squadron almost as soon as she reached Toulon and all three participated in a number of port visits and naval reviews.
All three participated in writing the manuscript.
All three participated in focus group facilitation and field note recording.
Similar(53)
ALL five participating managers continue to recommend diversified fund portfolios, even though diversification was a far from optimal strategy during much of the last seven years.
All three participating companies — Taylor 2, Ailey II and ABT II — performed together on opening night but will have their own individual programs through May 11.
What better way to celebrate Christmas!" The recording is available on iTunes and sales of the song support all three participating organizations.
Disagreements between two reviewers were resolved by consensus among all three participating reviewers.
Review showed that similar methods for specimen processing were used in all three participating laboratories.
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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