How many possibilities in tinyurl Looking at tinyurl, there is anywhere from 1 digit to 7 digits of I believe 36 choices (lowercase letters a to z and digits 0 to 9)

How do I calculate mathmatically the number of permutations of the string with 1 to 7 digits and 36 characters?

thanks,
Dean
The number of permutations (without replacement) of size $k$ on an alphabet of size $n$ is $n^k$. If you just need an approximate answer, the term $36^7$ is by far the largest, but if you want an exact answer, you can sum from $k=1$ to $k=7$.
I was just wondering the same thing.. Look up factorials - "The factorial $n!$ gives the number of ways in which $n$ objects can be permuted." 

Given $26$ characters and $10$ numerals, $36!= 3.72\times 10^{41}$,  a fair sized number! Tinyurl can repeat characters,  which reduces the overall combinations. 

I don't know if tinyurl does capital letters as well, but if they do then they aren't ever going to run out - $66!= 5.4\times 10^{92}$.