How many possible different base stat spreads fit the following criteria?

Question

The set "base stat spread" consists of exactly six integers. Each is between 1 and 255 inclusive. The total of all six members of this set must be between 180 and 780 inclusive. Please don't question my curiosity.

Comments

Or "How many different possible"

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So ranging from 1/1/1/1/1/1 to 255/255/255/255/255/255, with all numbers in between? Or 180/180/180/180/180/180 to 780/780/780/780/780/780?

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I actually have no clue what I'm doing but I plugged 180 and 780 into a combination calculator and got 3.34210013128995E+181 possible combinations.

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This had better satisfy Kero.

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I will have an answer for you in a few hours. I am currently formulating, and it is complicated because you used a non parallel range. I need to know if you meant BETWEEN 180 and 780 as you said (181-779) or if you meant "The total can be from 180 to 780."

Also, if I am going to put the effort in, I'd like to know the reason. If this is just for curiosity, then I will not share the results/waste my time. So... "Do not question my curiosity" can not apply.

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Most likely he just wants to know how many different pokemon, with different stat distributions, GF can make without going below 180 or above 780 BST. He says inclusive so I assume you should count 180 and 780 as well.

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It said "inclusive".

Answer 1

18 trillion, 480 billion, 712 million, 644 thousand 112, give or take.

Comments

Maybe you should provide your working and all, just so that we know you haven't inserted a random number :P

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Can't post photos. Basically just adjusted my dice Roller program to use the "exclude" function.
note* H=HPT, A=ATK, D=DEF, S=SAT, d=SDF, s=SPD
-        - I applied that to the following         
H≤255, H≥1
A≤255, A≥1
D≤255, D≥1
S≤255, S≥1
d≤255, d≥1
s≤255, s≥1

180≤(H+A+D+S+d+s)≤780

Then I plotted the potential for a single variable. H returned 154005938700.
       154,005,938,700
*                                   120
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18,480,712,644,112