Starfleet Psychological Division was an agency within the United Federation of Planets Starfleet which was responsible for reporting on the mental impact on a crew during starship travel. They were well aware that a crew of only three for a mission of twenty to twenty eight months had to be carefully chosen for compatability.
The Psych Division undertook a momumental task in analyzing personal traits and studying how they effected shipboard interactions in small groups under such remote circumstances. While Starfleet was waiting for the Psych Division's final accounting of how to select such specialized crews, they assembled some crews together, regardless of compatibility, justified by the need to keep Starfleet operating normally. (TOS - Worlds Apart novel: How Much for Just the Planet?)