1. Three commuter trains and four express buses depart from city A to City B in the morning, and three commuter trains and five express buses operate on the return trip in the evening. In how many ways can a commuter from City A to City B complete a daily round trip via bus and/or train?

2. The New Shanghai Restaurant offers a choice of four appetizers, five choices of soups, and twelve choices of entrees for its lunch special. How many different complete lunches can be ordered from the restaurant's lunch special menu?

3. A certain model of luxury car is offered with a choice of 16 exterior colors (10 metallic and 6 standard), 6 interior colors, and 3 trims. How many choices involving color and trim are available for the model?

4. An opinion poll is to be conducted among cable TV viewers. Six multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer finish the poll if exactly one response is given to each question?

5. An opinion poll was conducted by the Morris Polling Group. Respondents were classified according to their sex (M or F), political affiliation (D, I, R), and the region of the country in which they reside (NW, W, C, S, E, NE). (a) Use the generalized multiplication principle to determine the number of possible classifications.

6. A warranty identification number for a certain product consists of a letter of the alphabet followed by a seven-digit number. How many possible identification numbers are there if the first digit of the seven-digit number must be nonzero?

7. A password is to be made from a string of five characters chosen from the lowercase letters of the alphabet and the numbers 0 through 9.

(a) How many passwords are possible if there are no restrictions? (b) How many passwords are possible if the characters must alternate between letters and numbers?

8. Student Painters, which specializes in painting the exterior of residential buildings, has nine people available to be organized into three-person and six-person teams. Within a team, each person has a different job.

(a) Using the generalized multiplication principle, determine how many ways a three-person team can be formed? (b) Using the generalized multiplication principle, determine how many ways a six-person team can be formed? (c) Using your results from parts (a) and (b), determine how many ways the company can form either a three-person team or a six-person team from the available people?

9. To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four-digit code. If repetition of the same four digits is not allowed (for example 5555), how many possible combinations are there?