Editing Floor and ceiling functions (section)

===Number of strings without repeated characters===
The number of possible [[String (computer science)|strings]] of arbitrary length that doesn't use any character twice is given by<ref>{{OEIS el |1=A000522 |2=Total number of arrangements of a set with n elements: a(n) = Sum_{k=0..n} n!/k!.}} (See Formulas.)</ref>{{Better source needed|date=February 2022}} 

:<math>(n)_0 + \cdots + (n)_n = \lfloor e n! \rfloor</math>

where:

* {{math|''n''}} > 0 is the number of letters in the alphabet (e.g., 26 in [[English language|English]])
* the [[falling factorial]] <math>(n)_k = n(n-1)\cdots(n-k+1)</math> denotes the number of strings of length {{math|''k''}} that don't use any character twice.
* {{math|''n''}}! denotes the [[factorial]] of {{math|''n''}}
* {{math|''e''}} = 2.718... is [[Euler's number]]

For {{math|''n''}} = 26, this comes out to 1096259850353149530222034277.