I believe because she was the thirteenth applicant in a roomful of potential team members.

Yes, House was told to assemble a team of three, and he didn't want to bother with applications and interviews, so he took all 40 applicants and slowly whittled that down. He gave them numbers to wear around their necks. Instead of learning any of their names, he either gave them nicknames, or referred to them by the numbers on their chests.

Sort of like what Yang did with her interns on "Grey's Anatomy".

There was an episode where House helped out the CIA. The female CIA doctor accepted his offer to hire her. Did she ever show up in later episodes?

Good call. Come to think of it, I don't think so...

I'm not loving the addition of Amber Tamblyn to the cast. She must have a serious enemy in costume, too, because they're doing their best to make her look like crap.