Counting (10 points)
Use combinations and permutations to solve the following problems.
Clearly state
how you model the problem: If you count ordered or unordered
elements with or
without repetition, and what kind of combination or permutation you
use.
(a) A committee of three is chosen from a group of 20 people. How
many different
committees are possible if
i. (2 points) the committee consists of a president, vice
president, and
treasurer?
ii. (2 points) there is no distinction among the three members of
the
committee?
(b) (2 points) There are nine empty seats in a theater, and five
customers need to
find places to sit. How many different ways can these five seat
themselves?
(c) How many different ways are there to choose ten pastries from
the 20 varieties at
a bakery...
i. (2 points) ... such that no two pastries are of the same
variety?
ii. (2 points) ... if there are no restrictions? (I.e., multiple
pastries could be of
the same variety.)