This is an accurate calculation only if the 280 perks are completely independent. But it sounds like some of them are upgrades to perks. So, for instance, if perk #112 is an upgrade to perk #98, then it's not the case that you can combine #112 with 49 (or 79) other perks not including #98. So the number of possible combinations is somewhat less (how much less is difficult to say, without knowing more about what the perks are).
Yeah, that's very true. I thought about basing a generalized perk ruleset based off the skill trees in the Menu UI screenshot and seeing how many choices would arise based on that assumption. Maybe I'll do it later.
And then you have to take into account "real math" versus "game math," too. Out of all those possible configurations, how many are actually useful and how many would result in a character that was great only as long as you were roleplaying a theoretical researcher so socially gimped they couldn't survive 10 minutes outside a class lecture hall much less outside a city's walls?
The point isn't the viability or lack thereof of certain perk configurations, its the overall choice that it provides, that if someone REALLY wanted to play that way, they could. When I used to tabulate all the possible character configurations for Morrowind or Oblivion, I didn't force rulesets such as the player having to incorporate some form of offensive skill, because there are people out there who actually play such characters. Same is true for perks.