The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders’ meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members).
a) How many different slates 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 of directors are physicians. How many slates from part (a) have
(i) a physician nominated for the presidency?
(ii) exactly one physician appearing on the slate?
(iii) at least one physician appearing on the slate?
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