### MATH130: Quiz 4

**Name:**

You may use a calculator on this quiz. If you get stuck on a
question, move on to the next. If you have time left over at the end
of the quiz, check your work. There are questions on both sides of this page.

- (20 pts) A shopping mall labels parking spaces with a number
between 00 and 99 followed by a letter from A through F. How many
different such labels are possible?

- (20 pts) A baseball team has 12 players. How many different ways
can the team choose a starting lineup of 9 players, in order? (You
need not simplify your answer.)

- (20 pts) Five men and four women form a club. How many different
ways can they select an (unordered) steering committee for the club
consisting of 2 men and 2 women?

- (20 pts) Does the graph shown below have a path from
**a** to
**a** that passes through each edge exactly once? Justify your
answer. (Clarification: you *may* visit a vertex more than once.)

Bonus: (5 pts) Does the graph above have a path from **c** to
**d** that passes through each edge exactly once? Find such a path
or prove that there is none.