In 1994 the white house named Dr RuthR. Faden chairperson of the federal advisory committee of experts they assigned to do a report on the history and ethics of the government's radiation experiments on humans in the 1950's and1960's.
the sentence kind of says The committee ( of experts) that was being assigned doing, the committee can't assign itself, so eliminate A, D, and E, left B and C.
B. "to be assigned doing" I understand as the assignment was not assigned yet
C. The assigment was ongoing, presents the meaning of the sentence