Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

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.

Front

How do you apply the Fundamental Counting Principle?

Back

You multiply the number of options in each category.

Front

If an ice cream shop offers 3 types of cones and 31 flavors of ice cream, how many total combinations can a customer choose?

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93 combinations (3 cones × 31 flavors = 93).

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How many different ways can 8 violinists be seated in a row?

Back

40320 ways (8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320).

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

Back

36 possible outcomes (6 sides on the first die × 6 sides on the second die = 36).

Front

What does the Fundamental Counting Principle allow you to find?

Back

It allows you to find the number of total outcomes in your sample.

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What is a combination in the context of counting principles?

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

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What is a permutation in the context of counting principles?

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A permutation is an arrangement of items where the order does matter.

Front

If a shirt comes in 4 colors and 5 sizes, how many different shirts can be made?

Back

20 different shirts (4 colors × 5 sizes = 20).

Front

What is the formula for calculating permutations of 'n' items taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.