PoE took a shit and named it 2.8 trillion

LoL, tnx. But, still this can't be calculated without knowing the approximate number of active, support..etc gems which is probably loads.

The next question would be - how many sockets you can have max on your character from all the gear pieces?

Edit:
Also is there a limit to skill sockets an item can have? Same question for support gems?

In example:
Can an item (here's a guess as I dont have access to the game) with 3 sockets have all of them be for skills? Or will at least 1 socket be support? Or any other restrictions?

There are currently 46 skill gems and 30 support gems. Those numbers will easily double in the coming months.

I'm not positive what the current socket limits for gear are but these numbers should help.
helmet,gloves,boots - 4
shields - 3
armor,1-handed weapons - 6
some 1-handed weapons (wands, rapiers) - 3
2-handed weapons - 8

There are no restrictions on what sort of gems you put into sockets. Of course a support that isn't linked to a skill gem does nothing so you'll want at least 1 skill gem in a given item. I should also note that you only have 8 hotkeys for skills. You can have more skills but you'll need to swap them into a hotkey spot.

Counting sockets combinations you can have:

(all assumptions take 1(min)-4(max) helmet/glove/boots, 1-6 armor)

With shield+1h weapon with 1-6 sockets: 4`299`816`960 combinations

With 2 1h weapons each having 1-3 sockets: 358`318`080 sockets combinations

With 2h weapon having 1-8 sockets: 401`316`249`600 combinations

And thats sockets alone, not including any actuall gems in them

Edit:

That should give (if my calculations and assumptions are correct that is):
4,0597438464*10^11
socket combinations

with .92 socket limits are:

Head 4
Torso 5
Shield 5
Weapons 3
Hands 4
Boots 4
---------
25 on 6 slots

so a "build" could use 1 skill and 19 supports if you link the skill in every item of those 6 slots and the rest would be linked..
down to 25 skills without support - and a ton of combos in between.
Have fun getting numbers out of this :)

For skill setups:

This time assuming 0-4 sockets for helm\gloves\boots and 0-6 for armor:

With shield (0-3) and 1h weapon (1-6) you get 27! possible skill setups

With 2 1h weapons (0-3) you get 24! possible skill combinations

With 2h weapon (0-8) you get 26! combinations.

And that all doesnt include a single support gem.

So thats 1,129278135994669103579136*10^28 skill combinations

Never been good at math, but this is interesting stuff. BTW, Chris mentioned something about a new Strength passive which might allow dual-wielding two-handed weapons. Assuming we are discussing post 0.9.3 skills, that increases the potential slots available for these calculations. =^[.]^=

So far in total that would give something like:

2,93*10^179 combinations (more or less :P)

And thats including only passives, socket options on gear and skills you can allocate in said sockets, whitout a single support gem

The scores:

D3
2,800,000,000,000

PoE
293,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000

O.o Whiteboy... That's a lot of 0's. I cannot wrap my head around it ><