TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Eight different types of monthly commuter passes are offered by a city's local transit authority for three different groups of passengers: youths, adults, and senior citizens. How many different kinds of passes must be printed each month?

2. A coin is tossed four times and the sequence of heads (H) and tails (T) is recorded.

(a) Use the generalized multiplication principle to determine the number of outcomes of this activity.

Find all possible sequences:

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, and HTTT.

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, and HHHH.

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, and TTTT.

HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.

1. Four commuter trains and four express buses depart from city A to City B in the morning, and four commuter trains and three 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. A psychologist has constructed the following maze for use in an experiment. The maze is constructed so that a rat must pass through a series of one-way doors. How many different paths are there from start to finish?

3. In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Three different responses were allowed for each issue. Among the completed surveys, how many different responses to this survey were possible?

4. How many three-letter code words can be constructed from the first eight letters of the Greek alphabet if no repetitions are allowed?

5. The New Shanghai Restaurant offers a choice of 5 appetizers, 3 choices of soups, and 12 choices of entrees for its lunch special. How many different complete lunches can be ordered from the restaurant's lunch special menu?

6. Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a four-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured?

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

8. 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.

(b) Construct a tree diagram to exhibit all possible classifications of females.

NW, W, C, S, E, NE

FDNW, FDW, FDC, FDS, FDE, FDNE, FINW, FIW, FIC, FIS, FIE, FINE, FRNW, FRW, FRC, FRS, FRE, FRNE.

FDNW, FDW, FDC, FDS, FDE, FDNE, FINW, FIW, FIC, FIS, FIE, FINE, FRNW, FRW, FRC, FRS, FRE, FRNE, NW, W, C, S, E, NE.

FDNW, FDW, FDC, FDS, FDE, FDNE, FINW, FIW, FIC, FIS, FIE, FINE.

1. In recent years, a state has issued license plates using a combination of two letters of the alphabet followed by three digits, followed by another two letters of the alphabet. How many different license plates can be issued using this configuration?

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

(a) How many seven-digit telephone numbers are possible if the first digit must be nonzero?

(b) How many international direct-dialing numbers for calls within the United States and Canada are possible if each number consists of a 1 plus a three-digit area code (the first digit of which must be nonzero) and a number of the type described in part (a)?