my mother felt at fire station, the floor was to slippery, as a result she hurt her arm really bad so does she have a case here or not?

I'm curious as to why your mother was at the first station.  If she hurt her arm, did she require medical treatment?  The fire station may be immune from liability because of the nature of the use of the building.  It could also depend on whether the fire station is for volunteer firefighters, or for paid fire fighters that work for the state or the municipality.  Good Luck.