Let $n \geq 5$ be a natural number, let $X=\left\{x_{1}, x_{2}, \dots, x_{n}\right\}$, and let $Y=\left\{y_{1}, y_{2}\right\}$. Let $F$ be the set of functions from $X$ to $Y$ and $G$ be the set of bijective functions from $X$ to $Y$. Then
- The number of functions in $F$ equals $n^{2}$.
- The number of functions in $F$ equals $2^{n}$.
- The number of functions in $G$ equals $n^{2}-2$.
- The number of functions in $G$ equals $0.$
