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?

  • $\begingroup$ You have it. Just draw some pictures and use what might be called the fundamental principle of counting. $\endgroup$ – JP McCarthy Nov 19 '13 at 8:56

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