I have to explain this formula tomorrow in class and that catch is, I can't use algebra. I must solely use an "intuitive" explanation. But I don't know how to explain it!
$P(n,k) = C(n,k)k!$
I know that $P(n,k)$ is the # of ways of arrange $k$ objects from $n$ distinct objects with order. How can I "just say" that this equivalent to the # of ways to arrange $k$ objects from $n$ distinct objects without order multiplied by the number of ways to line them up $k$ ways? The people who I am trying to show are my 15-16 year old peers. They won't get this trust me! Any other way to explain it?