What is the chance of randomly generating a given 10-character sentence? Suppose we have an alphabet of the following allowed characters: 


*

*the lowercase letters $a$ through $z$ (26)

*the uppercase letters $A$ through $Z$ (26)

*the numerals $0$ through $9$ (10)

*the common punctuation marks:  $.,;:'"()!?-$ ( 11)

*the white space (1)


Making a total of 74 options. 
Each character $c$ in our 10-character sequence can be a member of the set of the allowed characters, $C$. 
Suppose we have a given ten-character sequence, $S$. (For the sake of example, let $S = Abc123.,!$)
What is the probability that a randomly constructed sequence, $S'$, (with each character being randomly selected from $C$) matches $S$?

Okay, so assuming repeat characters are allowed, we have a total of $26+26+10+11+1=74$ options for each character. This gives us #$options^n$ of characters needed. So in our case, we have $74^{10}=4,923,990,397,355,877,376$ options for the characters to match string $S$ exactly.
If repeated characters are not allowed, as character string $S$ leads me to assume, we may use $\frac{(\#options)!}{(\#options-n)!}$, or in our case, $\frac{74!}{(74-10)!}=2,606,955,172,242,220,800$ options for a non-repeating character sequence to match string $S$ exactly.
So to find the probability, we just do $\frac{1}{4,923,990,397,355,877,376}=2.03087317257* 10^{-21}\%$, or practically $0\%$ for all intents and purposes.
