2020 AMC 10A Problem 15

A positive integer divisor of 12! is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as \frac{m}{n}, where m and n are relatively prime positive integers. What is m+n?

\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 23

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.