Question 144
Let $m$ and $n$ be positive integers with $m \lt n$. Find the number of all injective functions $f: \{1, 2, \dots, m\} \to \{1, 2, \dots, n\}$ such that for any nonempty subset $A \subseteq \{1, 2, \dots, m\}$, the set of values $f(A)$ is different from $A$, i.e. $f(A) \neq A$. (A function $f$ is injective if $f(x) \neq f(y)$ when $x \neq y$.)