A post office is run by 2 clerks.

When person C arrives, A is served by one clerk and B served by the other. C gets served as soon as A or B leave (no one else waiting).

The time it takes server i to serve customers is exponentially distributed with mean 1/lambda(i) , i = 1, 2. lambda(i) = lambda subscript i

What is the expected time until all 3 customers have left the post office?

I need hint on how to start this problem.