In this book, the whole society is totally controlled by the government. The government decides, for example, when you are ready to raise a child and they decide what child you will get. It is the same way with jobs.
The job you will have is assigned when you become a Twelve. The Council of Elders has been watching you for the past few years. They have been watching what you like to do in your leisure time and in your volunteer work. They have been watching what you are good at. They assign your job based on what they notice.
As far as getting enough people, they just have to hope that there are people with the right aptitudes for the various jobs.