Question: The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockh olders meeting is scheduled to approve a new committee of company officers (chosen from the 10 board members).
a) How many different committees consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval?
b)Three members of the board are physicians. How many committees from part (a) will have: I. a physician nominated for presidency?
II.exactly one physician appearing on the committee?
III.at least one physician appearing on the committee?
I am not able to understand part b of this question because it is not clarified who are the physicians among the ten people.
Furthermore, if all possible committees in part a have exactly $3$ physicians(no matter how do I chose the persons, since no information is given about them), means that we have $9$ (at least) physicians out of $10$ persons which contradicts the 'exactly $3$' part.