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 options for each category. Here, there are 3 colors (red, green, blue) and 4 writing tips (bold, medium, fine, micro).
2. Recall the Fundamental Counting Principle, which states that if one event can occur in m ways and a second event can occur in n ways, then the two events together can occur in m × n ways.
3. Apply the principle by multiplying the number of color options by the number of writing tip options: $3\times 4$.
4. Calculate the product to find the total number of different pen choices available.
5. Interpret the result as the total number of unique pen combinations you can choose from this brand.

Key Concepts

Fundamental Counting Principle

The Fundamental Counting Principle states that if one event can occur in m ways and a second independent event can occur in n ways, then the total number of ways both events can occur is m × n. This principle helps calculate the total number of possible outcomes when combining choices.

Independent Choices

Independent choices mean that the selection of one option does not affect the selection of another. In this problem, choosing a pen color does not influence the choice of writing tip, allowing us to multiply the number of options for each category.

Counting Combinations

Counting combinations involves determining the total number of unique pairs or groups formed from different categories. Here, combining colors and tip types creates unique pen options, and the total is found by multiplying the number of colors by the number of tip types.