How many people do you need on a team to construct and program a robot drone?

Constructing a drone is not that hard, one person could easily do it. But not from scratch. You would use eg Arduino hardware and software libraries and look at other projects before starting on your own.
Constructing a hardened drone that works over long distances 24x7 in tough weather for years is something completely different - that takes a huge professional team. The mechanical issues are bigger than you might think. In fact, usually a lot bigger. Then of course there is the computer and the programming to be made as well.
If you look at amateur robot designers there are competitions in robot sumo, robot drones, robot football and much else. These robots only need to work as intended for a short while and are usually made by one or a few persons in their spare time. But to win larger championships you would need a sponsor, an extensive mechanical workshop and at least a few friends.