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The phrase "all three types of" is correct and usable in written English.
It can be used when referring to a specific set of three categories or classifications of something.
Example: "In our study, we examined all three types of renewable energy sources: solar, wind, and hydro."
Alternatives: "all three categories of" or "all three kinds of".
Exact(60)
You need all three types of networks.
WRKY33 was upregulated by all three types of biotic stress.
And they found examples of all three types of spreading.
All three types of uncertainty come from incomplete knowledge.
Finally, another important category of transcription factors affected by all three types of pathogens was WRKYs.
All three types of proportion coexist and interact in sculpture, contributing to its expressiveness and beauty.
She added all three types of intelligence were important for the success of an individual.
Terborgh's team periodically surveyed the vegetation of all three types of island.
For all three types of presentations, this slot will be 90 minutes.
One-quarter of the sample experienced all three types of abuse.
The DOBA end-group exhibits strong affinity to all three types of filler.
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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