I REALLY need help with this probability equation!

SarahKreme

Okay, so... I'm not sure this is even the proper place to post this, but I do know this is the proper place to possibly find the answer to this, being that I'm sure there are people who are MUCH BETTER at math than I am....

So, I play this game, and I've pretty much got everything down, but it's a very very VERY "CHANCE" heavy game.... like, you know, upgrading your equipment starts at 10%, and you can get it boosted up to 50% total, that stuff is easy for me, but then there are OTHER THINGS that have began to confuse me, and I want to know the total number of combinations POSSIBLE for any one item, and then I need someone to figure out the chance of me getting the one combination I'm looking for on a 5 line piece of equipment....

This is basically how it works...

Eye accessory
LUK% 1
DEX% 2
INT% 3
STR% 4
ALL STATS% 5
Accuracy 6
Avoidability 7
W.DEF (% or number) 8+9
M.DEF (% or number) 10+11
Max HP/MP 12+13

There isn't just 13 values above, there are 26 because I can either get a unique line, or legendary line, and I can only get 5 of these lines, which means I could get luk% dex% str% int% and all stats%, but any of those lines could either be unique lines or legendary lines.

(Note, unique is 9%, legendary is 12%)

So it may look like THIS:
luk 12% or 9%
dex 9% or 12%
str 9% or 12%
int 12% or 9%
all stats 9% or 12%

Now here's where the math actually comes in, and this is the part I don't understand...
I need to know the probability of getting 3 lines of int 12% on a five line piece of equipment...
SO I want my equipment to look like this(Sort of)

int 12%
int 12%
int 12%
anything!
anything!

I know there are 26 values, and I need to go down the line multiplying by the next number like 26*25*24*23 (etc. etc. etc...)

BUT I don't know how to figure out the PROBABILITY of getting the 3 lines I WANT. Could someone please help a girl out? PLEASE?!?!? :<

ALSO It would be GREATLY appreciated if you gave me the equations you used to determine the out comes as well, if you wouldn't mind!

mfb

As a good approximation, you can neglect items with 4 or more 12%-int. In that case, you can calculate the probability of (12%int, 12%int, 12%int, something else, something else) in that order - just multiply the individual probabilities. And then you have to multiply the result with 15, as there are 15 possible positions for those 3 12%int-stats.

In a similar way, you get items with 4 times 12%-int by calculating the probability of (12%int, 12%int, 12%int, 12%int, something else) and a factor of 5 (5 options where "something else" can appear), and items with 5 times 12%-int (no additional factor here).
Add them, and you are done.

You might consider 4 times 9%-int as well, as it could be similar to 3 times 12%-int.