The City of Ember/Fridge

Fridge Logic
If jobs are assigned randomly, why don't we see any women working in the pipeworks?
 * Lina was going to work there, before she swapped jobs with Doon.
 * We do. Read the books. Doon's supervisor is a girl, for one.

Fridge Horror

 * If the power finally did go out in Ember with everyone there.
 * Supposedly, it did. Lina asks how many people were "left behind" in the second book, and the reply is "Too many", which leads one to believe that some were left in the city.
 * In The City of Ember, the plan was to live in the underground city for 200 years, but due to government conspiracy gone wrong they don't know how to get out, or even that they should get out. The city is falling into decay and food supplies are running low. Canned food supplies. Canned food supplies which were never replenished. Had they gotten out when they were originally supposed to, they would still have been eating 200-year-old canned food. Even Twinkies don't last that long.

Fridge Brilliance
While the random process of choosing people for jobs doesn't make much sense, it does lend a lot of credence to why the city is in such crappy condition - all the times when people with very little technical skill got put into technical jobs.