Question

Let $A$ and $B$ be any two sets such that $n\left(A\right)=p$ and $n\left(B\right)=q$, then the total number of functions from $A$ to $B$ is equal to

Answer 1

If set $A$ has $p$ elements and set $B$ has $q$ elements

then number of Function from $A$ to $B$ is

$\left[n\right(B){]}^{n\left(A\right)}=q^p$.

Hence, the number of function is $q^p$.