5
$\begingroup$

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!?

$\endgroup$
6
$\begingroup$

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:

$$n^1 + n^2 + n^3 + ... + n^k = \frac{n^{k+1}-1}{n-1}-1$$

$\endgroup$
  • $\begingroup$ That means 62^7? $\endgroup$ – mehulmpt Aug 15 '14 at 13:11
  • $\begingroup$ @MehulMohan there are exaclty $62^7$ strings with exactly length $7$, but if you want to include those with length $1, 2,3,4,5$ and &6& you have to add them up. Check my edit for a simpler way to compute it. $\endgroup$ – Darth Geek Aug 15 '14 at 13:16
  • $\begingroup$ Genius! Thanks bro! $\endgroup$ – mehulmpt Aug 15 '14 at 13:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.