Fundamental Counting Principle

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What is the Fundamental Counting Principle?

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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.

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If a music streaming service offers 10 playlists and 3 subscription plans, how many combinations can a user choose?

Back

30 combinations (10 playlists × 3 plans = 30).

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How many outfits can be made with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

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80 outfits (5 jeans × 8 t-shirts × 2 shoes = 80).

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What is the formula to calculate combinations of two independent choices?

Back

The formula is: Total combinations = (Number of choices for first option) × (Number of choices for second option).

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If a wardrobe has 15 pairs of slacks and 23 shirts, how many combinations of slacks and shirts can be made?

Back

345 combinations (15 slacks × 23 shirts = 345).

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How many different versions of a car model can be created with 4 trim levels, 5 colors, and 3 interiors?

Back

60 versions (4 trims × 5 colors × 3 interiors = 60).

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A pizza restaurant offers 12 meat toppings and 5 vegetable toppings. How many ways can you select one topping?

Back

17 ways (12 meat + 5 vegetable = 17).

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What is the significance of the Fundamental Counting Principle in problem-solving?

Back

It simplifies the process of counting combinations by allowing multiplication of independent choices.

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If you have 3 types of bread and 4 types of cheese, how many sandwich combinations can you make?

Back

12 combinations (3 breads × 4 cheeses = 12).

Front

What is an example of a real-world application of the Fundamental Counting Principle?

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Choosing outfits from a wardrobe, planning meals with different ingredients, or selecting options for a product.