Pigeonhole Principle

Hello! I am taking an advanced math class and would like to include the following in my paper, however I am having a difficult time figuring it out.  I searched the web and the Khan site and there is very little help out there.  Can you help me?

I have a 40 bed hospital unit, (20 rooms with two beds each)
Following conditions apply for cohorting roommates:
only males can be roomed with males
only females can be roomed with females
patients with MRSA can only be roomed with patients with MRSA
patients with ESBL can only be roomed with patients with ESBL
(10 possible combinations)

How do I apply the pigeonhole principle to this? Thank you for looking at this.