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 do both.

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How many ways can you answer a true/false question?

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There are 2 ways to answer a true/false question: True (T) or False (F).

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If a quiz has 4 true/false questions, how many ways can you answer them?

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For 4 true/false questions, the number of ways to answer is 2^4 = 16.

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How many ways can you answer 3 multiple choice questions with 4 options each?

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For 3 multiple choice questions, the number of ways to answer is 4^3 = 64.

Front

What is the total number of ways to answer a quiz with 4 true/false and 3 multiple choice questions?

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Using the Fundamental Counting Principle: 16 (true/false) × 64 (multiple choice) = 1024 ways.

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What is a combination in the context of choices?

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A combination is a selection of items where the order does not matter.

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How many combinations are there for choosing 1 sandwich from 3 options and 1 drink from 2 options?

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Using the Fundamental Counting Principle: 3 (sandwiches) × 2 (drinks) = 6 combinations.

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If you roll two dice, how many possible outcomes are there?

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There are 6 sides on each die, so the total outcomes are 6 × 6 = 36.

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If you roll a die and flip a coin, how many possible outcomes are there?

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There are 6 outcomes from the die and 2 from the coin, so total outcomes are 6 × 2 = 12.

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

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Using the Fundamental Counting Principle: 5 (jeans) × 8 (t-shirts) × 2 (shoes) = 80 outfits.