FTCE Professional Education Practice Exam

Which of the following is not a technique used to find the number of elements in an event or sample space?

1. Counting principle

2. Permutations

3. Combinations

4. Subtraction method

The correct answer is: Subtraction method

The subtraction method is not typically a recognized technique for determining the number of elements in an event or sample space. Instead, it is generally used in scenarios where one needs to find the difference between two quantities or sets, rather than directly counting elements. The counting principle is a foundational approach in combinatorics, which states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the total number of ways the two events can occur together is 'm × n'. This principle is crucial when calculating the size of sample spaces. Permutations and combinations are also specific techniques used to count arrangements and selections, respectively. Permutations focus on the arrangement of objects where order matters, while combinations deal with selection where order is irrelevant. Both are methods based on the counting principle that provide systematic ways to find the number of outcomes in a given situation. Each of these techniques—counting principle, permutations, and combinations—has clear applications in counting elements, whereas the subtraction method does not align with this objective.