Posts are picked by Cadets walking up to a row of large bulletin boards or walls, filled with index cards with the names of units/posts. At the start of the process the boards are filled with index cards, indicating the plethora of choices - Italy, Germany, Hawaii, Ft. Carson, etc.. Cadets are called up in Order of Merit and pick a single card, indicating their choice for their first duty assignment, and the OIC announces the pick. Kind of like the NFL Draft.
As the end nears, there are routinely the same few cards remaining for the last few Cadets to choose - Ft. Drum, Alaska, and Ft. Polk. Occasionally an individual will have circumstances that lead to them to having a preference for Ft. Drum or Alaska, but I have never heard of anyone holding their breath hoping Ft. Polk is still on the board when their turn comes.