A few less than you think.
One male per each end of a hose - but hoses can do double duty, you often wont be using them all at once. Also, some really only need a QD connector on one end - a bog standard hose clamp is fine for things that dont really need to be switched and changed on any given brew day.
eg - the hose that goes from your wort cooler into your fermenter. Might have a connector ex the chiller, but the end dangling in the fermenter doesn't need one. Or the hoses that go to and from your HERMS heat-ex. Do they really need to disconnect from the heat-ex? Why? Does the hose from your HLT have to come off the HLT? Why?
Ask yourself that question for every connection in your brewery and you'll find that there are a fair few that really dont need camlocks or any other sort of QD - a hosetail and a cable tie will do the job.
Especially for you - you're going to run a brew-troller, so I assume you will want all your connections connected all at once so the machine can do the switching. So exactly what is it you are going to need to connect or disconnect "quickly"? One or two things tops. You are going to need to run a CIP cycle to get all those valves and stuff clean... so you dont even need to easily pull anything much apart to clean it, it all gets cleaned where it is. OK sure, every now and again you'll want to strip things down... but if 3 out of 4 connections in your brewery are simple half inch compression fittings, or hoses connected with hose clamps - thats going to cost you what - 15mins of wielding a shifter every few months? versus buying expensive camlocks that you'll only operate a few times a year.
I say have a good hard think - only buy the QDs for connections you are 100% sure you are going to have to operate at least once on every brewday. If you're wrong, you can always buy more QDs, but no one's going to give you your money back for ones you bought and find you never use.
TB