How quickly do LLCs fill up?

I got accepted into the honors college at George Mason and I would like to join the Honors LLC. They said they are on a first come first served basis depending on how soon you submit your enrollment and housing fees. I’m still waiting to hear back from some colleges and I have to wait until April. Will the LLCs be full by then since they have a limited capacity?

“Honors College freshmen who wish to live on campus are automatically placed into the Honors Living Learning Community (LLC) housed in the Commons. Placement is on a first-come, first-serve basis according to the date freshmen submit their housing application and $300 deposit. No additional LLC application is required. Honors College freshmen are placed in the Commons until it reaches capacity. Later applicants will still have the option to join another living learning community or choose to live amongst the general freshmen population.”
http://honorscollege.gmu.edu/prospective-students/llc/