Yep, maybe even less, it is also 24/7, rule of the thumb is that for each position 5 (depending on the contract/mansion even 6) people are needed, to cover holidays, leaves, illnesses, etc., in a year there are 8760 hours, and hours worked are rarely more than 1800 or so.
I bet the number of people working at a given time is more like 15,000.