### MATH130: Quiz 4

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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.

1. (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?

2. (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.)

3. (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?

4. (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.