Find total number of mappings

Question

Let $A$ be a set of $n$ elements and $B$ be a set of $m$ elements. Show that the total number of mappings from $A$ to $B$ is $m^n$.

Answer 1

For each element of $A$ you should choose an element of $B$. You can choose an element of $B$ in $m$ different ways. This should be done repeatedly for $n$ times. So the result $m^n$. Try with $n=1$ and $n=2$ to understand.