Answer
Makes sense.
Work Step by Step
The contrapositive of $p\rightarrow q$ is $\sim q\rightarrow p$.
The converse of $p\rightarrow q$ is $q \rightarrow p$.
The inverse of $p\rightarrow q$ is $\sim p\rightarrow q$.
Thus the inverse of the converse is $\sim q\rightarrow p$, which is the contrapositive, thus the statement makes sense.