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I am defining a word by a n character sequence.

In English (for the purposes of my paper), I am assuming the following:

  • The alphabet is only the 26 characters alpha characters, lowercased
  • Digits are only 0-9 (10 total)
  • A space is allowed

Therefore, how many 5-n combinations can I have?

I believe this is a [combinatorial][1] problem but I haven't really found any resources that would give me a way to attack this problem (that I can understand).

I did find this post which would make me think:

I need to do something like: 26 * 10 * 1 * 5! but I don't think that is right. Where 26, 10, 1 all represent the possibilities of inputs and 5! is the size?

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1 Answer 1

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There is a famous combinatorics formula defined as $\binom{n}{r} = \frac{n!}{r!(n - r)!}$

For your problem, you have 37 distinct characters, and you want to know the amount of combinations that can be made of these characters where each combination has a length of 5. To use the formula, we let $n = 37$ and $r = 5$.

Simply, apply these numbers in the given formula.

$\binom{37}{5} = \frac{37!}{5! * (37 - 5)!} = 435897$

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