How could you find the number of different arrangements of 6 letters in a computer password?

Answer 1

First you decide how many different symbols may be used. For example, with only lowercase letters, there are 26 symbols. If you permit lowercase and uppercase, there are 52 symbols. If you include digits too, that increases to 62. If you include a few special symbols (such as period, coma, hyphen, etc.), you will get a few more. Then you raise that to the power 6, since in each position you can have (for example) 26 different possibilities, and the possibilities are independent. That is, with only lowercase letters, you have 26 options for the first position, 26 options for the second, etc., resulting in 26 x 26 x 26 x 26 x 26 x 26 = 266. This assumes there are no additional restrictions as to what letters you can use - for example, there may be repeated letters.

If on the other hand 6 specific letters are given, and you must rearrange them, the number of possibilities is only 6 x 5 x 4 x 3 x 2 x 1. This is written as 6! (the factorial of 6).