1. 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 presi
dent, vice president, secretary, and treasurer can
the board present to the stockholders for their ap
proval?
(b) Three members of the board are physicians. How
many slates from part (a) have (i) a physician nom
inated for presidency? (ii) exactly one physician
appearing on the slate? (iii) at least one physician
appearing on the slate?
2. How many arrangements are there of all the letters in
SOCIOLOGICAL?
3. In how many diﬀerent orders can ﬁve runners ﬁnish a
race if no ties
allowed?
4. A club has 25 members
(a) How many ways are there to choose four members
of the club to serve on
an executive committee?
(b) How many ways are there to choose a president,
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 Fall '09
 MarniMishna
 vice president, college food plan

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