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I am looking at this formula

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I want to first make sure that I understand the principle. This is saying that, if I wanted to find out all the ways I could order the letter of the alphabet into a 26-letter string, then the answer is 26!.

If the formula for permutations of size k is this: k-permutations = n! / (n-k)!

Then, why isn't the formula for permutations of size 1 this: n! / (n-1)!

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The formula for permutations of size 1 is $n! / (n-1)! = n$, which makes sense; if there are 26 letters, there are 26 ways to choose one letter.

The formula in the text is for permutations of size n from a set of n items, that is, for $k = n$. Indeed, $n! / (n-k)! = n! / (n-n)! = n!$.

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  • $\begingroup$ Gotchya. You're saying, the number of ways I can order a 52-card deck is 52! $\endgroup$ – Cauder Mar 27 at 1:43
  • $\begingroup$ Yes, that is what I'm saying. $\endgroup$ – Noah Mar 27 at 1:56

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