Question: 2015 Fall Midterm - 1
The Carleton Computer Science Society has a Board of Directors consisting of a President, two
Vice-Presidents, and a five-person Advisory Board. The President cannot be Vice-President and cannot be
on the Advisory Board. A Vice-President cannot be on the Advisory Board. Let $n$ be the number of
students in Carleton's Computer Science program, where $n \geq 8$. In how many ways can a Board of
Directors be chosen?
(a)
$(n-5){n \choose 2}{n-1 \choose 5}$
(b)
$(n-7){n \choose 2}{n-2 \choose 5}$
(c)
$(n-2){n\choose 2}{n-2 \choose 5}$
(d)
$n{n \choose 2}{n \choose 5}$