A student chooses two distinct real numbers $x$ and $y$ with $0<x<y<1$.

The student then attempts to draw a triangle $ABC$ with:

Which of the following statements is/are correct?

I For some choice of $x$ and $y$, there is exactly one triangle the student could draw.

II For some choice of $x$ and $y$, there are exactly two different triangles the student could draw.

III For some choice of $x$ and $y$, there are exactly three different triangles the student could draw.

(Note that congruent triangles are considered to be the same.)

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