# Why is the formula for permutations of size one n!

I am looking at this formula

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)!

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, $$n! / (n-k)! = n! / (n-n)! = n!$$.