Assignment:
Multiplication Principle Problems
Q1. Commuter Passes. Five different types of monthly commuter passes are offered by a city’s local transit authority for each of three different groups of passengers: youths, adults, and senior citizens. How many different kinds of passes must be printed each month?
Q2. Coin Tosses. A coin is tossed 4 times and the sequence of heads and tails is recorded.
a. Use the generalized multiplication principle to determine the number of outcomes of this activity.
b. Exhibit all the sequences by means of a tree diagram.
Q3. Commuter Options. Four commuter trains and three express buses depart from city A to city B in the morning, and three 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?
Q4. Health-Care Plan Options. A new state employee is offered a choice of ten basic health plans, three dental plans, and two vision care plans. How many different health care plans are there to choose from if one plan is selected from each category?
Q5. Code Words. How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?
Q6. Automobile Colors. The 2007 BMW is offered with a choice of 14 exterior colors (11 metallic and 3 standard), 5 interior colors, and 4 trims. How many combinations involving color and trim are available for the model?
Q7. License Plate Numbers. Over the years, the state of California has used different combinations of letters of the alphabet and digits on its automobile license plates.
a. At one time, license plates were issued that consisted of three letters followed by three digits. How many different license plates can be issued under this arrangement?
b. Later on, license plates were issued that consisted of three digits followed by three letters. How many different license plates can be issued under this arrangement?
Q8. Warranty Numbers. A warranty identification number for a certain product consists of a letter of the alphabet followed by a five-digit number. How many possible identifications numbers are there if the first digit of the five-digit number must be nonzero?
Q9. Lotteries. In a state lottery, there are 15 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder can win more than one prize?
Provide complete and step by step solution for the question and show calculations and use formulas.