Name:      

Directions: Show all work.

1. [2.5 points] How many ways are there to make a list $(x_1,\dots ,x_5)$ where each $x_i$ is a digit in $\{0,\dots ,9\}$ and we have $4$ even digits and one odd digit? For example, $(0,0,1,8,6)$ and $(2,2,4,6,3)$ count but $(0,1,2,3,4)$ and $(0,0,0,0,0)$ do not.

2. [2.5 points] How many integers in $\{1,\dots ,1000\}$ have no repeated consecutive digits?

3. [2.5 points] Count the functions $f:\{1,\dots ,9\}\to \{1,2,3,4\}$ such that $f(1)=f(t)$ for some $t\in \{2,\dots ,9\}$.
4. [2.5 points] How many integers in $\{1000,\dots ,5000\}$ are even and have all distinct digits?