"three distinguishable" is correct and usable in written English.
For example: "The three distinguishable elements of the painting created a unique and captivating visual."
The theory of distribution involves three distinguishable sets of questions.
Roundworms have a thick, flexible cuticle, with three distinguishable zones, covered by an epicuticle.
Anatomically the ear has three distinguishable parts: the outer, middle, and inner ear.
It will be noted that 3He forms three distinguishable liquid phases of which two are superfluids (see superfluidity), while 4He may exist only as two distinct liquids of which one is a superfluid.
Classical phenomenologists practiced some three distinguishable methods.
Work loss attributable to headache has three distinguishable components.
Four of the, more or less, nine distinguishable black nations did accept independence and full self-government.
Within days, a single case, one distinguishable and atomized and unknown, became iconic.
An estimated 10 30 million distinguishable species currently inhabit this sphere of life, or biosphere.
Because of their different "colours" each quark comes in three varieties, and there are eight distinguishable gluons.
In passerines, the feathers are arranged in eight distinguishable tracts, with apteria (relatively bare skin) between them.
