The Transition Matrix Below Shows the Probabilities That Customer Switch

Multiple Choice

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. $$\begin{array}{l}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Next Week }\\\begin{array} { l c c } \text { This Week } & \text { Don's } & \text { Limmer's } \\\hline \text { Don's } & 0.9 & 0.1 \\\text { Limmer's } & 0.2 & 0.8\end{array}\end{array}$$ If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's?

A) 333
B) 400
C) 667
D) 1000
E) 1600