Let $n$, $m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\{1, 2, , n\}$ of size $k$. Consider sampling a function uniformly at random from the set of all functions mapping $\{1, , n\}$ to $\{1, , m\}$. What is the probability that $f$ is not ... $1 - \frac{k!{n\choose k}}{n^k}$ (E) $1 - \frac{k!{n\choose k}}{m^k}$

asked
Mar 24
in Combinatory
zxy123
3.6k points
11 views