If there are $r$ roses and $c$ carnations, then $3r + 2c = 50$

Since $2c$ and $50$ are even, $3r$ is even, so $r$ must be even; find how many even $r$ work

Let $r$ be the number of roses and $c$ the number of carnations, so $3r + 2c = 50$ with $r, c \ge 0.$

Because $2c$ and $50$ are even, $3r$ must be even, forcing $r$ to be even. The largest possible $r$ is $16$ (since $3 \cdot 17 \gt 50$), so $r \in \{0, 2, 4, \ldots, 16\}.$

That gives $9$ values of $r,$ each determining a bouquet.

Thus, the correct answer is C.