$A$ has 4 elements and $B$ has 3. How many onto functions are there from $A$ to $B$?

Explanation

1. 01

   Two elements of $A$ share an image: choose them, ${}^{4}C_{2} = 6$ ways.

2. 02

   Then match the 3 groups to the 3 images: $6 \times 3! = 36$.