# Proof of Permutations

With repetition allowed,

You multiply the r number of times for total n objects

n * n * n ...


When the repetion is not allowed then you take away an object each time

n * (n - 1) * (n - 2) ....


So where does the proof come from that you have to multiply that times with number of objects?

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Try to elaborate what the question is; currently I can't understand it – Gadi A Jun 6 '11 at 6:36
Difference between the binomial distribution (replacement) and the hypergeometric distribution (without replcaement) perhaps? – Juan S Jun 6 '11 at 6:49
My question is, how do you know that multiplying will get you the number of ways? is there any proof? – user753214 Jun 6 '11 at 7:03

http://en.wikipedia.org/wiki/Rule_of_product Are you meaning this? You can resort to Cartesian product and cardinal numbers in set theory.

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This is what I was talking about. – user753214 Jun 6 '11 at 10:18
@user753214, if you think this is a good answer, you can vote it up, you can even accept it. If it's not good enough for you to do that, you can explain what more you need. – Gerry Myerson Jun 6 '11 at 12:45

I am assuming you are trying to pick up $r$ numbered balls from a total of $n$ balls, and you are looking for the number of ways to do this such that the ordering of the balls is relevant.

Suppose repetition is allowed, this means that you pick up one ball from the urn(?) and then put it back and then repeat the process. There are $n$ ways of doing it in the first step and for each of those $n$ ways, there are another $n$ ways of doing it in the next step and so on so forth for $r$ steps.

In the second case, when repetition is not allowed, the urn progressively loses balls, so there are $n$ ways in the first step, $n-1$ in the second, etc.

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