Question 12
Let $A = \{1, 2, 3, 4\},$ and let $f$ and $g$ be randomly chosen (not necessarily distinct) functions from $A$ to $A.$ The probability that the range of $f$ and the range of $g$ are disjoint is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m.$