Math 184A
Final Exam
Fall 2003
•
Please put your name and ID number on your blue book.
•
CLOSED BOOK, but you may have TWO PAGES of notes.
•
Calculators are NOT allowed.
•
You need not simplify the arithmetic in your answers.
•
You must show your work to receive credit.
1. (8 pts.) In each case,
give an example or explain why none exists
.
(a) A permutation
f
of
{
1
,
2
,
3
,
4
,
5
}
such that
f
20
is not the indentity permutation.
(The identity permutation is the function
g
such that
g
(
x
) =
x
for all
x
in the
domain.)
(b) A simple graph with 5 vertices and 12 edges.
2. (16 pts.)
Committees are to be formed from 5 Democrats and 8 Republicans.
A
committee must be as balanced as possible; that is, the number of Republicans and
Democrats on the committee must be as equal as possible.
(a) How many ways can a 7 member committee be formed?
(b) How many ways can both a 7 member committee and a 5 member committee be
formed if no person can be on both committees?
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 Fall '08
 staff
 Math, pts, blue book

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