# Help me understand theorem for combinations with repetition intuitively.

I have the following theorem in my textbook:

There are $C(n + r − 1, r) = C(n + r − 1, n − 1)$ r-combinations from a set with n elements when repetition of elements is allowed.

Where $C(n + r - 1, r) = \frac{(n+r-1)!}{(r)!(n-1)!}$

First, I don't understand how you get to this formula. Second, I don't understand why there is an equivalence between $n-1$ and $r$ above. Third, why factorial?

Thanks!

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There’s a pretty decent explanation of that formula here. The fact that $\binom{n+r-1}r=\binom{n+r-1}{n-1}$ is an immediate consequence of the general fact that $\binom{n}k=\binom{n}{n-k}$, something that you should have encountered a while ago if you’re looking at this theorem. –  Brian M. Scott Mar 2 at 22:20