Very possible. The one college degree could be a medical doctorate degree and they could exchange eggs, brussel sprouts and home made boots for the care. No citizen would be denied care because with 100 people, you don't need to lose anyone.
Darn, our one doctor is an orthopedic surgeon and you have a tumor in your left lung. . . now what?
Or alternatively: Oh darn, our one doctor is a heart surgeon and you just got a spiral fracture to the leg. . . now what?
What about the anesthesiologist, the nurses, the team who fixes the MRI machine when it breaks, the assisting surgeon, the other several dozen people who make modern medicine work.
Everyone could have equal medical care, but it would be equally crappy medical care. Who's gonna pay the boots, brussel sprouts and eggs to provide medical care for the one 90 year old guy who cannot contribute anymore to your small society? Lots of people would probably volunteer, but what if he's kind of a jerk?
Also, being a doctor is hard work, why can't he just STOP being a doctor and grow his own darn brussel sprouts? Are you going to FORCE him to be a doctor simply because he knows how? Even if he could do better for himself by dropping that proffession when it becomes unprofitable?
With 1 doctor, there is no such thing as a 'second opinion', there is also no such thing as: the price is too high. If he wants to charge 3 pairs of boots, or 100 pairs of boots, it's not like you can say: "No I'll have someone else remove my appendix."
do you not have to take good care of everyone of the 100? Do you not need to keep the 100 strong and healthy as possible?
Not really. Some of them are probably completely useless, and in fact, a burden on the rest of you.
And it depends on what your goal is. Do you want to repopulate the earth? Well then you better stop worrying about the old people and start having lots of babies.
My personal goal would be pretty much the same as it is now. Namely: For me to have the best quality of life I can. That definately does not include raising a bunch of children in a post-apocolyptic world.
I personally wouldn't give a crap about saving the species or anything like that, and if I had good reason to believe that I could have a better life out by myself, I wouldn't think twice about leaving the whole group and living elsewhere.
With 100 different people from 100 different backgrounds, odds are pretty slim you're gonna have many people who are willing to strive towards the same goal you are trying to reach.