Problem:

There are eleven computer science students in a classroom with ttwelve seats arranged in a 4x3 rectangle. There is a window on one side of the room. The students always sit in a way which satisfies the following conditions:

☼ Ken is always the first to class and sits in the front row.
☼ There are four students in the class named Dan. No two Dans sit next to or behind one another.
☼ Sean always sits next to the window.
☼ The one girl in the class sits in a corner. She never sits behind a Dan.
☼ Phil sits next to Sean and does not sit next to the girl.
☼ Tim never sits in the front half of the class.
☼ One of the Dans wears a fedora and puts his coffee on the empty desk beside him.
☼ The person who sits behind the empty desk is not named Dan.
☼ Another student brings a longboard to class and arrives late. He sits in the last seat, which is diagonal Fedora's coffee desk, but not behind Fedora.
☼ The person behind Fedora is not Sean, Phil, Longboard, or Tim.

How likely is it that a student chosen at random from the back row is named Dan?