Somehow related to Exponential distribution?

Consider a post office with 2 clerks. Three people, A, B, and C enter simultaneously. A and B go directly to the clerks, and C waits until either A or B leaves before he begins service. What is the probability that A is still in the post office after the other two have left when

1)the service times are i with probability 1/3, i = 1, 2, 3?
2)the service times are exponential with mean 1/u? [I get how this is exponential distribution]

I'm not sure what to do with part 1. I don't really know how to approach it.

You can list the scenarios where A would still be there.

A stays 3 and B and C each stay 1.

That's the only case. With probability (1/3)(1/3)(1/3)=1/27.

No exponential distribution required.

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