This number was never explicitly stated on the show, but it was estimated based on:
* The size of the ship: The Enterprise was a large vessel, capable of carrying a significant crew.
* The various departments: The ship had numerous departments, each requiring a certain number of personnel, including Starfleet officers, enlisted personnel, and civilian specialists.
* The roles of the characters: The show featured a limited number of recurring characters, which represented only a small fraction of the entire crew.
It's important to remember that this number is an approximation. The actual crew complement might have varied depending on the specific mission and the needs of the ship at any given time.