Mathematics ACT Aspire Practice Test

What does the Fundamental Counting Principle help determine?

1. The range of possible outcomes

2. The number of ways to arrange items without order

3. The number of possible outcomes in a sample space

4. The average outcomes of an event

The correct answer is: The number of possible outcomes in a sample space

The Fundamental Counting Principle is a foundational concept in combinatorics that enables the calculation of the total number of possible outcomes when there are multiple stages or choices involved in an event. According to this principle, if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the total number of outcomes for both events occurring is the product of the individual outcomes (m × n). This principle is particularly relevant when determining the size of a sample space consisting of multiple independent choices. For instance, if one were to examine the possible outcomes when selecting a shirt and then selecting a pair of pants, where there are 3 shirt choices and 4 pant choices, the total number of outfit combinations would be calculated as 3 (shirts) × 4 (pants) = 12 possible outfits. The other options do not accurately capture the essence of the Fundamental Counting Principle. The range of possible outcomes focuses on the extent of results but does not quantify them. Arranging items without order pertains more to permutations and combinations, where the order is not considered, which is a different aspect of counting. The average outcomes associated with an event don’t relate to counting outcomes directly but involve statistical measures like means, which is outside