Morrowind had us select 10 skills that "defined" our class, while Oblivion gave us 7, but despite that, there was nothing stopping us from going outside of those chosen skills to just level up every skill in the game. Now, such a practice has become even encouraged, by removing a definitive "class" system that makes you tag an arbitrary number of skills, and you just do whatever you want, and it all counts towards your overall progress,
So I began thinking... if I am given free reign to every skill in the game, and they all contribute to the growth of my character, just how unique can I make my character? Thinking of it from my non-math brain, I looked at it as "There are roughly 10 skills or so that I want to use on my character - that's more than HALF of the available skills in Skyrim! Just how can I make my character something unique if I'm using over half of the available skills on my character? Doesn't that make me a rather Superman-ish 'Jack of All Trades' that's skilled in every playstyle???"
Well... sure, I guess, if you are narrowing the game down to simply 3 playstyles (Warrior, Mage, Thief), and their very narrowly defined sub-playstyles (Battlemage, Nightblade, Stealthy Warrior [what would the term for this be?])
But the math says otherwise. I called up my friend who is a math wiz (math major in college, very skilled in very advanced math), and I brought up the predicament to him, and we went through the formulas, and came up with the solution that if one were to select 10 skills out of 18, there would be over 7000 possible combinations of skills. That's not including the even further specialization with perks and what they will add. And that of course doesn't count all the different possibilities of creating a character less than 10 skills, or the different possibilities of creating a character with more than 10 skills.
My friend's response was that, if you added up ALL the different possibilities of character builds, from players who build characters focusing on just 1 skill (probably never going to happy, but certainly a choice), to characters focusing on all 18 skills, and every possible combination in between, as well as the possible combinations that come from the perks system, his words "you'd have a [censored] amount of possibilities".
Needless to say, I feel that my worries of building a generic character that really has no uniqueness because I chose a certain number of skills are subsided at the moment.