DJ has 5 pairs of shoes. How many ways are there for DJ to wear his shoes over a week if he doesn't want to wear the same pair two days in a row?

Let $A=\left\{1,2,3,4\right\}$  and  $B=\left\{1,2,3,4,5\right\}$ . How many functions  $f:\ A\to B$  exist?

Let $A=\left\{1,2,3,4\right\}$  and  $B=\left\{1,2,3,4,5\right\}$ . How many one-to-one functions  $f:\ A\to B$  exist?

Let $A=\left\{1,2,3,4\right\}$  and  $B=\left\{1,2,3,4,5\right\}$ . How many onto functions  $f:\ A\to B$  exist?

A bijective function is a function that is both one-to-one and onto. Let $f:\ A\to B$  be a bijective function. Which of the following are true?