$2.(10$points$,$a:$8,$b:$2)$Consider$$a$$perfect$$crystal$$in$$which$$all$$of$$the$$lattice$$sites$$are$$occupied$$by$$quantized$$identical$$ particles.$$If$$the$$crystal$$contains$$four

particles,$$which$$are$$located$$on$$four$$lattice$$sites$,$and$$the$$total$$energy$$is$$U$=4$u$,$a$)$how$$many$$distributions$$and$$microstates$$they$$individually$$contain$?$b$)$How$$many$$macrostates$$they$$ contain?$$