How calculate the number of possible different variations? I feel stupid, but I don't know how to calculate how many possible variations I can get from for example three spaces (1|2|3) Normally I'd say: "well that is easy, just take the number of spaces (=3) and 3^3"
But that doesn't work with two spaces, like "1|2", there are only 2 different ways on how to arrange two numbers, but 2^2 would be 4. 
(I want to know how many spaces I need to get ~25000 possible variations)

A note on terminology and notation...
There are two words you want to learn here, permutations and combinations.
Permutations are how many distinct arrangements can be made from a set, so (1,2,3) and (3,2,1) are different. 
$$^nP_r = P^n_r = \frac{n!}{(n-r)!}$$
Combinations are how many subsets you can form from a set, so (1,2,3) is the same as (3,2,1), same elements.
$$^nC_r = C^n_r = \binom{n}{r} = \frac{n!}{r!(n-r)!}$$
Often combinations are spoken as "$n$ choose $r$", as they are the measure of how many choices there are from a set.  So the UK National Lottery is a choice of 6 balls from 49, so the number of ways to choose this is "49 choose 6".
$$^{49}C_6 = \binom{49}{6} = 13,983,816$$
