Problem 60 - College Algebra

Question

Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem.

Step-by-Step Solution

Answer

There are 24 different combinations to choose a full meal, if considering one item from each category, according to the Fundamental Counting Principle.

Step 1 - Understand the Fundamental Counting Principle

The Fundamental Counting Principle states that if there are \( m \) ways to do one thing, and \( n \) ways to do another, then there are \( m \times n \) ways of doing both.

Step 2 - Develop the problem

Problem: A fast food restaurant offers 3 types of sandwiches (Chicken, Beef, Vegetarian), 4 kinds of drinks (Coca-cola, Sprite, Water, Juice), and 2 kinds of desserts (Cake, Ice-cream). How many different meal combinations can a customer order?

Step 3 - Apply the Fundamental Counting Principle

According to the Fundamental Counting Principle, the total number of different meal combinations can be found by multiplying the number of chocies in each category. So in this case, it would be \( 3 \text{ sandwhich choices} \times 4 \text{ drink choices} \times 2 \text{ dessert choices} \).

Step 4 - Calculate the number of combinations

Calculating this gives \( 3 \times 4 \times 2 = 24 \) different meal combinations.