$A$ has 3 elements and $B$ has 5. How many one-one functions are there from $A$ to $B$?

Explanation

1. 01

   The images must all differ: 5 choices for the first element, 4 for the second, 3 for the third.

2. 02

   ${}^{5}P_{3} = 5 \times 4 \times 3 = 60$.