FTCE Professional Education Practice Exam

What does the counting principle state?

1. n + m

2. n - m

3. (n)(m)

4. n / m

The correct answer is: (n)(m)

The counting principle states that if there are \( n \) ways to perform one action and \( m \) ways to perform a second action, and the actions can be performed in sequence, then the total number of ways to perform both actions is given by multiplying the number of ways to perform each action, which is represented as \( (n)(m) \). This principle is fundamental in combinatorics and is often referred to in problems where you are determining the total number of outcomes resulting from multiple independent events. For instance, if a student has 3 different shirts and 2 different pairs of pants, by using the counting principle, the student can create \( (3)(2) = 6 \) unique outfits. This principle helps in simplifying the process of counting combinations and permutations in various scenarios. Other options do not appropriately represent the relationship being described in the counting principle.