1 .
Carleton's Computer Science program has $f$ female students and $m$ male students, where $f \geq 1$
and $f + m \geq 8$. The Carleton Computer Science Society has a Board of Directors consisting of a
President, five Vice-Presidents, and two Cider-Presidents (whose task is to buy cider for the
President). All members of the Board of Directors are Computer Science students. The President is
female, cannot be Vice-President, and cannot be Cider-President. A Vice-President cannot be Cider-President.
In how many ways can a Board of Directors be chosen?
(a)
$f \cdot {f+m \choose 5} \cdot {f+m \choose 2}$
(b)
$f + {f+m-1 \choose 5} + {f+m-6 \choose 2}$
(c)
$f \cdot {f+m-1 \choose 7}$
(d)
$f \cdot {f+m-1 \choose 5} \cdot {f+m-6 \choose 2}$