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Difficulty: EasyCounting Principles

Match each counting scenario to the mathematical concept that is used to solve it.

  • Selecting a 3-person cleaning crew from 8 volunteersCombination
  • Choosing 1st, 2nd, and 3rd place winners in a spelling beePermutation
  • Picking 1 sandwich, 1 side item, and 1 drink from a lunch menuFundamental Counting Principle

Answer

The cleaning crew matches to Combination, the spelling bee winners matches to Permutation, and the lunch menu matches to the Fundamental Counting Principle.
Each scenario perfectly aligns with the core definition of its matching counting principle based on whether order matters, and whether the events are sequential and independent.

Step-by-Step Solution

1
Analyze the volunteer scenario to determine if order matters.
It matches to a Combination.
Because the members of a cleaning crew have identical roles, selecting Person A then Person B is exactly the same as selecting Person B then Person A.
2
Analyze the spelling bee scenario to determine if order matters.
It matches to a Permutation.
Since 1st, 2nd, and 3rd places are distinct, the arrangement or sequence of the winners matters.
3
Analyze the lunch menu scenario to identify the counting structure.
It matches to the Fundamental Counting Principle.
The scenario involves a sequence of independent events (choosing from different categories), which requires multiplying the number of choices.

Key Concept

Distinguishing between combinations (order does not matter), permutations (order matters), and the Fundamental Counting Principle (multiplying independent events).
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Topics

Counting Principles

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