PROBLEM SET \#1 (MATH)- FUNDAMENTAL COUNTING PRINCIPLE
Instructions: All the problems involve real-life scenarios applying the concept of the fundamental counting principle. Each problem is worth 10 points. Write the problem and your answer on a long bond paper. Submit on or before MARCH 15, 2024.
1. Draw a tree diagram to determine the number of possible outcomes.
1.1 A choice of muffin or donut with coffee, milk, or juice.
1.2 Basketball uniform in white, red, blue, or green in sizes small, medium, large.
2. A multiple choice has four questions. Each question is answered with \( a, b, c \), or d. How many outcomes are possible?
3. In relation to \( \# 2 \), suppose the multiple-choice test has five questions. How many sets of answers are possible?
4. Five dice are rolled. How many outcomes are possible?
5. You have a choice of one main dish, one vegetable, and one beverage. The main dish choices are lobster, chicken, fish, or steak. The vegetable choices are ampalaya, lettuce, or broccoli. The beverage choices are cola, tea, or pineapple. How many dinners are possible?
6. In relation to \#5, how many outcomes show lobster? If you include lemonade as a beverage choice, how many dinners would be possible?
7. Adrian is planning to buy a new car. The dealer gave him a brochure about the options. How many combinations are possible with a choice one exterior color (red, black, white, or orange), one interior upholstery (leather or cloth), and one accessory package (power door locks, air-conditioning, or cd player?
8. In relation to \#7, if Adrian decides he wants an orange car, how many combinations are possible now?
9. There are 4 commuter trains and 5 express buses departing from town \( A \) and town \( B \) in the morning and 3 commuter trains and 4 express buses operating on the return trip in the evening. In how many ways can a commuter from town \( A \) and town \( B \) complete a daily round trip via bus and/or train?
10. How many four-digit numbers can be formed from the sets \( \{0,1,2,3, \ldots\} \) if zero cannot be the first digit and the given conditions are satisfied?