The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders' meeting is scheduled

Question:

The board of directors of a pharmaceutical 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?
Corporation
A Corporation is a legal form of business that is separate from its owner. In other words, a corporation is a business or organization formed by a group of people, and its right and liabilities separate from those of the individuals involved. It may...