Use the Fundamental Counting Principle to solve Exercises 29–40. A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

Verified step by step guidance

1. Identify the number of choices for each category: colors and writing tips.
2. There are 3 color options: red, green, and blue.
3. There are 4 writing tip options: bold, medium, fine, and micro.
4. Apply the Fundamental Counting Principle, which states that if there are \( n \) ways to do one thing and \( m \) ways to do another, then there are \( n \times m \) ways to do both.
5. Multiply the number of color options by the number of writing tip options to find the total number of different pen choices.

Key Concepts

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 × n ways to perform both actions. This principle is essential for calculating the total number of outcomes in scenarios involving multiple independent choices.

Combinations of Choices

In this context, combinations of choices refer to the different options available for each category of selection. Here, the colors of the pen and the types of writing tips represent two separate categories, and the total number of combinations is found by multiplying the number of options in each category.

Multiplication of Independent Events

When dealing with independent events, the total number of outcomes is determined by multiplying the number of outcomes for each event. In this case, the choice of pen color is independent of the choice of writing tip, allowing us to use multiplication to find the total number of pen options.