LOS ANGELES (CBS) — Police say an instructor at a security-guard training class was shot to death by a student in a downtown Los Angeles classroom Wednesday.

The 44-year-old instructor was taken to a hospital where he died, Los Angeles police spokeswoman Karen Rayner said.

Police said that one of the students in a class of 12 at the Coast Career Institute got up and left during the class. Moments later, he kicked in the door, walked back in with a gun and shot the instructor.

The shooter then dropped the gun and walked out of the classroom.

Arriving police officers found the shooter standing outside the building, calmly smoking a cigarette. The shooter allowed the officers to cuff and arrest him without incident.

The instructor's name has not been released.

Police late Wednesday identified the alleged shooter as 22-year-old Law Thien Huynh of Gardena.

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