I'm working on a programming algorithm and need a little math help. I'm in 10th grade and I think the question I'm asking is actually a permutation and combination logic question. Okay, so I've 62 characters as follows:
0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ
I want to know how many unique characters can be made from this?
For example, for length 1 character, there could be 62 unique characters.
Length 2 character, there could be 00,01,02,03….AA,AB,AC…FA,FB,FC,FD…ZA,ZB,ZC…0A,0B,0C…,etc.
I hope you are getting me what I'm trying to say.
And the maximum length of the string should be 7 characters.
So, in total, how many unique random strings can be generated from these 62 characters!?
Best Answer
Using $n$ unique characters, there are exactly $n^k$ strings of length $k$.
Think of it this way:
You have $n$ choices for the first character, $n$ for the second one... $n$ for the $k$-th one.
So the amount of options is
$$\underbrace{n·n·n\ldots n}_{k\text{ times}} = n^k$$
If you want to know the amount of strings with $n$ unique characters with length up to $k$ then you need to add:
$$n^1 + n^2 + n^3 + ... + n^k = \frac{n^{k+1}-n}{n-1}$$