# How to determine the amount of n possibilities of a word?

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?

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