$50$ Points. Consider adjacent oilfields A and B operated for units A and B$,$ respectively. There are six

oil rigs for the two oilfields, three assigned for each oilfield. Three out of the six rigs are state$-$of$-$the art machines with better productivity, and thus the business unit prefers. Consequently, general

management set the following policy to avoid internal disputes: $$before a new week starts, randomly

select one rig on each oil field and swap them.$$ We are interested in modeling the weekly number of

state$-$of$-$the$-$art rigs operated by business unit B as Markov chain.