Fundamental Counting Principle

After studying Module 3: Lecture Materials & Resources, discuss the following:

Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem. Respond to at least 2 of your classmates.

• Your initial post should be at least 200 words/numbers or a combination of both. Your initial post is worth 60 points.
• Additional readings must be cited, and formatted in the current APA style.
• You should respond to at least two of your peers by extending or adding supplementary distinctions to their posts.

Problem Using 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 to do both. Let’s create a problem that illustrates this principle.

Problem Statement: Imagine a local coffee shop offers a special promotion where customers can create their own coffee drinks. There are 3 types of coffee bases (Espresso, Americano, and Cold Brew), 4 types of milk (Whole, Skim, Almond, and Oat), and 2 types of flavor syrups (Vanilla and Caramel). How many different combinations of coffee drinks can a customer create if they can choose one type of coffee base, one type of milk, and one type of flavor syrup?

Solution: To find the total number of combinations, we can apply the Fundamental Counting Principle.

• The number of ways to choose a coffee base: $m=3$ (Espresso, Americano, Cold Brew)
• The number of ways to choose a milk: $n=4$ (Whole, Skim, Almond, Oat)
• The number of ways to choose a flavor syrup: $p=2$ (Vanilla, Caramel)

Using the Fundamental Counting Principle, the total number of combinations $C$ can be calculated as follows:

$$C=m\times n\times p=3\times 4\times 2=24$$

Thus, a customer can create 24 different combinations of coffee drinks.

Conclusion

The application of the Fundamental Counting Principle allows us to systematically determine the total number of combinations possible when making selections from multiple categories. In this scenario, understanding these combinations can enhance customer experience and promote creativity in drink choices.

References

To support your post, ensure to include any relevant readings or resources that align with the problem and its solution, formatted in APA style. Here’s a general citation format you might use if you have specific sources:

Author, A. A. (Year). Title of work: Capital letter also for subtitle. Publisher. DOI or URL (if applicable