Messysaurus wrote:Why wouldn't the number of string possibilities be 140^27 instead of 27^140 (first sentence)? My thought process: if you were to look at numbers 1-1000, there are 10 characters and with a length of 3 characters; 10^3 = 1000 possibilities, not 3^10 = ~57k. I apologize in advance if I'm missing something obvious.

You're right that with a length of 3 characters and 10 possible digits for each of those characters, there are 10^3 = 1000 possibilities. You're just getting the application wrong when it comes to the twitter situation. For the 3 character, 10 digit case, we have length = 3 and possible characters = 10, and the number of possible strings is calculated by

possible strings = (possible characters)^(length) = 10^3 = 1000

For the twitter case, we have length = 140 and possible characters = 27, so indeed

possible strings = (possible characters)^(length) = 27^140

and not 140^27.