Please work this problem showing all steps so that I can understand it.

Assume there is a three story aviary at a local zoo which houses 400 small birds. The aviary has three levels, and the birds spend their day ying around from one favorite perch to the next. Thus at any given time the birds seem to be randomly distributed throughout the three levels, except at feeding time when they all y to the bottom level. Assume that whenever a bird is on any level of the aviary, the probability of that bird being on the same level 5 minutes later lSl/z. If the bird is on the first level, the probability of moving to the second level in the next 5 minutes is 1/4. For a bird on the second level, the probability of moving to the rst level in the next 5 minutes is 1/3. Finally, for a bird on the third level, the probability of moving first in the next 5 minutes is 1/6. a. Suppose that immediately after breakfast all the birds are in the dining area on the first level. Where are they in 10 minutes? b. Find the steady state for the position of the birds if it ex1sts