Disregarding the number of available types, how many different eeveelutions can there possibly be?

Question

What defines an Eeveelution is;
1) A single-typed Pokemon that evolves from Eevee
2) Its base stats follow a distribution of 130-110-95-65-65-60

How many different Eeveelutions can there theoretically be provided that each one had a different distribution of those base stats?

Comments

I want to know using the power of math, the least number of eeveelutions there can be if each one had a different arrangement of stats.

Answer 1

#720 actually.
The formula you should be using is this;
nPr, meaning n!/(n-r)!
n represents the amount of values, and r represents the amount of values that you actually take. Since in this case, you have 6 values, but you take all 6. The formula nPr is used when order matters and repetition is not allowed.
What do I mean by order mattering?
If order does not matter the combination [3,23,62] would be the same as [23,3,62]
However when order does matter the combination [3,23,62] would be different from [23,3,62]

So subbing this into the formula
= 6!/(6-6)!
Please note that ! in maths represents "Factorial" - this means you must multiply the number by every single positive integer under it, not including 0 since that technically isn't either positive nor negative e_o
= 720/0! (0! is equal to 1. This is the exception to the explanation I gave above about !)
= 720

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Well, Jojo tested this on your calculator and I think we know the source of your problem now
There are two 65s, so the online calculator factors them as "duplicates"

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Extra Stuff

>If you factor in types, allowing dual types, would that restrict the number?
hmmm...
Just wondering
aren't there 18 types...
commented 15 hours ago by Helios_Ex

If we were to take dual types, then the amount of possible eeveelutions that are possible is equivalent to the amount of possible dual types + amount of possible single types.
What is this?
6P2 + 18
= 153 + 18
= 171

So if we were to factor in types, allowing dual types, top of 171 eeveelutions.

Comments

Complete and Perfect.  Thank you

Answer 2

This is quite scary. Using http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html to work out how many theoretical Eeveelutions there can be through just re-arranging the 130-110-95-65-65-60 stats.

There can be ..................... 360 different Eeveelutions! and they all will still have the 130-110-95-65-65-60 and all with a different distribution of those stats.

GAMEFREAK, you can make Eeveelutions till the year 20XX and they won't share their stats with another.

Comments

If you factor in types, allowing dual types, would that restrict the number?
hmmm...
Just wondering
aren't there 18 types...