The Fundamental Counting Principle is a core idea in combinatorics that allows us to find the number of ways a series of events can occur. It states that if you have a series of events, and each event can occur in a number of distinct ways, the total number of different outcomes for the sequence of events is the product of the number of outcomes for each event.
So, if we were to apply the Fundamental Counting Principle step by step:
1. First, identify the sequence of events and how many different outcomes can occur in each individual event. For example, if Event 1 can happen in 3 different ways, and Event 2 can happen in 2 different ways, and so on.
2. Next, to find the total number of different outcomes for the entire sequence of events, you would multiply the number of outcomes for each event. Continuing with our example: 3 (outcomes for Event 1) multiplied by 2 (outcomes for Event 2) equals 6 total combinations for the sequence of events.
Based on this explanation, the correct statement about the Fundamental Counting Principle is:
A. The total number of outcomes in a sequence of events is the product of the number of outcomes in each event.
Choices B, C, and D are incorrect interpretations of this principle. The sum of the number of outcomes (choice B) would be used in a situation where events are alternatives to each other, not a sequence. Dividing (choice C) or subtracting (choice D) the number of outcomes doesn't correspond to any mathematical principle related to counting outcomes of sequences of events.
