the numer of partial function between two sets in combinatoric way $A$ and $B$ two sets. $|A|=k, |B|=n.$ I need to prove in a combinatoric way that the number of partial function from $A$ to $B$ is $(n+1)^k.$ I thing the number is $Σ(n^i),$ for $i=0$ to $k.$ but I have no idea how to show equality, and how to prove it in
a combinatoric way.
If someone can show me the way or guide me that will be great!
thanks for helpers.

HINT: Let $p$ be some object not in $B$, and let $B'=B\cup\{p\}$.


*

*Explain why there are $(n+1)^k$ functions from $A$ to $B'$.  

*Find a bijection between the set of partial functions from $A$ to $B$ and the set of total functions from $A$ to $B'$. (Think about how you might interpret $f(a)=p$ if yo want to convert the function $f:A\to B'$ into a partial function from $A$ to $B$.)

