If we have 3 books A, B, and C, there are 3! = 6 possible arrangements. With 1 book there is 1 arrangement, which makes sense.

But with 0 books (nothing at all), we also say there is 1 arrangement. That feels strange to me. If we count “emptiness” as one arrangement here, why not add it everywhere, like in the case of 1 book instead of 1 we should say it is 2....one for the book itself and the other one for the empty arrangement.

I thinks 0! should be 0, or that we should just leave 0! undefined, the way some operations are left undefined elsewhere in math. Instead of being forced to defined illogically (philosophy speaking) claiming we get forced.