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Basically what I want to know is how you derive $$\frac{n!}{r!(n-r)!}$$ from the number of combinations of $r$ objects in n places. Essentially I couldn't work out why it was and just need an explanation. Any help appreciated. Thank you.

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marked as duplicate by GNUSupporter 8964民主女神 地下教會, N. F. Taussig combinatorics Jan 14 at 22:54

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  • $\begingroup$ there are n! total ways to permute the n objects. But you can permute the r indistinguishable objects in r! ways. Likewise with the (n-r)! spaces that are not occupied by anything. $\endgroup$ – Justin Stevenson Jan 14 at 22:43

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