How many rabbits can I keep in my rabbit run?

I currently own a chicken run for several poultry, a 15" by 12" roofed chickenwire 'cage' with a garden shed for shelter during the night. I will be looking to move these into a larger better free range system so I have been thinking about converting the area to a rabbit run. I'm planning well ahead, I have no experience with rabbits so I want to try owning one first, but I'd like to know just how many rabbits I'd be able to keep. The shed can have the various hutches they need but I wanted to put them out into the run during the day to give them a more natural lifestyle. I'm not looking to keep hundreds of rabbits - I'm never out for tonnes of money - just say five females and a buck. Is this possible or will they all start fighting once they are out? As I said they'll be in separate hutches during the night but its the day period where they'd be loose that I'd like to know about. Any other info would be great. Thanks!